Answers
Answer:
351.5625
1,440,000
Step-by-step explanation:
\(\boxed{\begin{minipage}{7 cm}\underline{General form of an Exponential Function}\\\\$y=Ae^{kt}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $k$ is a constant.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}\)
Given:
Doubling period = 15 minutesAt t = 120 minutes, y = 90,000(Let t = time in minutes).
If the doubling period is 15 minutes, then at t = 135 minutes, y = 180,000:
\(\implies 90000=Ae^{120k}\)
\(\implies 180000=Ae^{135k}\)
Divide the second equation by the first to eliminate A, and solve for k:
\(\implies \dfrac{180000}{90000}=\dfrac{Ae^{135k}}{Ae^{120k}}\)
\(\implies 2=\dfrac{e^{135k}}{e^{120k}}\)
\(\implies 2=e^{135k} \cdot e^{-120k}\)
\(\implies 2=e^{15k}\)
\(\implies \ln 2 = \ln e^{15k}\)
\(\implies \ln 2 =15k \ln e\)
\(\implies \ln 2 =15k\)
\(\implies k=\dfrac{1}{15}\ln 2\)
Substitute t = 120, y = 90000 and the found value of k into the formula and solve for A:
\(\implies 90000=Ae^{\left(120 \cdot \frac{1}{15}\ln 2\right)}\)
\(\implies 90000=Ae^{\left(8\ln 2\right)}\)
\(\implies 90000=Ae^{\ln256}\)
\(\implies 90000=256A\)
\(\implies A=\dfrac{90000}{256}\)
\(\implies A=351.5625\)
Therefore, the function that models the scenario is:
\(\large\boxed{y=351.5625e^{\left(\frac{1}{15}t \ln 2\right)}}\)
So the initial population at time t = 0 was:
351.5625To find the size of the bacteria population after 3 hours, substitute t = 180 into the found formula:
\(\implies y=351.5625e^{\left(\frac{1}{15}(180) \ln 2\right)}\)
\(\implies y=351.5625e^{\left(12 \ln 2\right)}\)
\(\implies y=351.5625e^{\left(\ln 4096\right)}\)
\(\implies y=351.5625 \cdot 4096\)
\(\implies y=1440000\)
Therefore, the size of the bacterial population after 3 hours was:
1,440,000The initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
If n₀ is the initial size of a population experiencing exponential growth, then the population n(t) at time t is modeled by the function:
n(t) = n₀(e\()^{rt}\)
Where r is the relative rate of growth expressed as a fraction of the population.
Given:
Doubling period = 15 minutes
At t = 120 minutes, n(t) = 90,000
If the doubling period is 15 minutes, then at t = 120+15 = 135 minutes,
90000 = n₀(e\()^{120r}\)
18000 = n₀(e\()^{135r}\)]
To find the r:
Take ratio of both of the equations,
90000 / 18000 = n₀(e\()^{120r}\) / n₀(e\()^{135r}\)
2 = (e\()^{135r}\) . (e\()^{-120r}\)
r = 1/15 ln2
Substitute the value of r, t and y.
90000 = n₀(e\()^{120r}\)
90000 = 256n₀
n₀ = 351.5652
Now, the function
n(t) = n₀(e\()^{rt}\)
n(t) = (351.5652)(e\()^{(1/15)(180)(ln2)}\)
n(t) = 1440000
Therefore, the initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.
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Related Questions
Can I get some help please!
Answers
Answer:
n = -3
Step-by-step explanation:
-5 = -8 - n
3 = -n
-3 = n
please help me ill give brainliest
Answers
Answer:
D
Step-by-step explanation:
help please :) ........................................
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Answer:
y > 14 third
Step-by-step explanation:
A bakery sells 11 types of sandwiches. Here are their calorie amounts 279,595, 597, 599, 601, 603, 608, 611, 617, 617, 950. Identify all values that are outliers
Answers
Answer:
279 and 950
Step-by-step explanation:
Outliers are numbers that are significantly greater or lesser than the other numbers in the data set.
The other numbers are very close together on a numerical scale, with the exception of 279 and 950.
Therefore, these two numbers are the outliers.
The outliers are 279 and 950
Outliers:Outliers are numbers that are significantly more or lesser as compared to the other numbers in the data set.The other numbers are very nearest together on a numerical scale, having the exception of 279 and 950.So, these two numbers are considered to be the outliers.Learn more about the outlier here: https://brainly.com/question/9933184?referrer=searchResults
the product of two rational numbers is 9.6 if one rational number is 66/7. find the other rational number
Answers
Answer:
0.1714
Step-by-step explanation:
just substract 9.6 from 66/7 which will give u the other rational number.
then add both the rational numbers to check ur answer.
66/7 + 0.1714 = 9.6
How many terms does the expression r ÷ 9 + 5.5 have?
Answers
Answer:
3 terms
Step-by-step explanation:
The number of terms in the given expression is 2.
The given expression is r ÷ 9 + 5.5.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Here, in the expression r/9 +5.5, there are two terms
They are r/9 and 5.5
Hence, the number of terms in the given expression is 2.
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What is 20% of 50 apples
Answers
Answer:
10
Step-by-step explanation:
Answer:
10 apples
Step-by-step explanation:
20% of 50 = 10
10 apples
Solve the inequalities and compare 2x+6<10
Answers
Answer:
x<2
Step-by-step explanation:
2x+6<10
2x<10-6
2x<4
x<4/2
x<2
Combine like terms to simplify the expression:
12 + 3y − 8 − 7y =
Answers
Answer:
4-4y
Step-by-step explanation:
2
Stuart uses 3 of a cup of sugar for a recipe. How many cups of sugar are needed for 7 recipes?
Express the amount as a mixed number.
cups
Blank 1:
Blank 2:
Answers
Answer:
Blank1=4 blank2=2\3
Step-by-step explanation:
2\3 for 1 recipe
For 7 recipe = 7 x 2\3
= 14\2 x 2\3 -> take out the 2
14\3 = 14 divided by 3 is 4 with remainder of 2
So, 4 2\3
A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.
A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 6 to 10 that stops at 3, for 11 to 15 that stops at 5, for 16 to 20 that stops at 6, and for 21 to 25 that stops at 1. There is no shaded bar for the 1 to 5 interval.
Which of the following best describes the spread of the data?
Explain its meaning in this situation.
The data has a possible range of 19, which is a wide spread. This might mean that the most common number of water-skiing trips is 10.
The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
The data has a possible range of 6, which is a narrow spread. This could mean that most of the students have taken a similar number of water-skiing trips.
The data has a range of 6, which is a narrow spread. This might mean that the most common number of water-skiing trips was 6.
Answers
Answer:
(b) The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
Step-by-step explanation:
You want the best description of the spread of data shown in the histogram.
SpreadThe least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...
range = max - min = 25 -6 = 19
This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.
__
Additional comment
The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)
<95141404393>
Ringani worked overtime to raise a total amount R30 000.00 to settle his student debt. If he has deposited R8 500.00 yearly into an account earning 7,04% interest per year compounded annually. How long, rounded to one decimal place did it took her to accumulate the total amount? A. 3.0 years B. 2.4 years C. 2.8 years D. 2.0 years
Answers
It took Ringani 2.8 years to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.
To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the time in years
In this case, we have:
P = R8,500.00
A = R30,000.00
r = 7.04% = 0.0704 (in decimal form)
n = 1 (compounded annually)
We want to find the value of t.
Using the formula, we can rearrange it to solve for t:
t = (log(A/P)) / (n * log(1 + r/n))
Substituting the given values, we have:
t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))
Calculating this using a calculator, we find that t is approximately 2.8 years.
Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.
The correct answer choice is C. 2.8 years.
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Question
In the diagram, ACDE - AGHI Find the value of y.
с
G
11 cm
( x - y) cm
650
D
H
E
Z
Answers
Answer:let me get these points :))
Step-by-step explanation:thanks <3
jddkffkfffkkfkkf
What is the meaning of "the notion of finiteness"?
Answers
The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.
In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.
In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.
This concept is essential to the development of computer programs that are efficient, reliable, and secure.
In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.
In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.
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what should be added to 6x²+9x-8 to obtain 4x²-8x+6 ?
Answers
Hence, in answering the stated questiοn, we may say that As a result, we equatiοn must add (2x - 1)2 + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.
What is equatiοn?A algebraic equatiοn is a strategy fοr linking twο prοpοsitiοns and expressing equivalence using the equals symbοl (=). A mathematical sentence that shοws the equivalency οf twο fοrmulas is knοwn as an equatiοn in algebra. In the calculatiοn 3x + 5 = 14, fοr example, the equal sign puts a space between the values 3x + 5 and 14. Tο describe the relatiοnship between the twο sentences printed alοng either side οf a letter, a mathematical fοrmula can be utilised. Usually, the insignia and the prοgramme are the same. 2x - 4 = 2, fοr example.
Tο identify what shοuld be added tο 6x² + 9x - 8 tο create 4x² - 8x + 6, we need tο undertake a methοd called "cοmpleting the square".
We can cοnclude frοm cοmparing the twο fοrmulas that a = 4, b = -8, and c = 6.
Sο we must "finish the square" by adding and remοving a term equal tο (b/2a)2. In this instance, we have:
(b/2a)² = (-8/2(4))
a² = 1
4x² - 8x + 6 + 1 - 1
(4x² - 8x + 1) + (6 - 1) (6 - 1)
(4x² - 8x + 1) is a perfect square trinοmial, which may be factοred as (2x - 1)².
As a result, the ultimate sοlutiοn is:
6x² + 9x - 8 + 1 - 1 + (2x - 1) (2x - 1)
a² + 5
As a result, we must add (2x - 1)² + 5 tο 6x² + 9x - 8 tο get 4x² - 8x + 6.
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PLS HELP ASAPPPPPPP
I NEED HELP
Answers
The tables which shows a proportional relationship between x and y are table 3 and table 4.
Which table shows a proportional relationship between x and y?Using ratio to find the proportional relationship
Table 1
x : y = 8 : 8
= 1 : 1
x : y = 12 : 10
= 6 : 5
Not proportional
Table 2:
x : y = 2 : 3
x : y = 3 : 8
Not proportional
Table 3:
x : y = 5 : 3
x : y = 10 : 6
= 5 : 3
Proportional
Table 4:
x : y = 4 : 1
x : y = 16 : 4
= 4 : 1
Proportional
Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.
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four triangles are formed by joining the midpoints of three sides of an equilateral triangle
Answers
Answer:
all are congruent
Step-by-step explanation:
Four triangles are formed by joining the mid points of the three sides of a triangle then all are congruent as sides of all triangles will be same as they are formed by joining the mid points.
3 The lyy Hill Sunshine Club collected 524 cans for a canned food drive. The cans were then split up equally into 8 boxes. (a) Part A How many cans were in each box? Part B How many cans were left over after the boxes were filled? (b) А 65.5 cans < NEXT
Answers
Answer:
sorry I wish I could it help you but if you have any other question let me know
need an answer for this
Answers
What is the equation of the line that is perpendicular to the line defined by the equation 2x = 4y – 8 and goes through the point (1, 2)?
Answers
The equation of the perpendicular line is y = -2x + 4
How to determine the line equation?The line equation is given as:
2x = 4y - 8
Make y the subject
4y = 2x +8
Divide by 4
y = 0.5x + 2
The slope of the above equation is
m = 0.5
The slopes of perpendicular lines are opposite reciprocals.
This means that, the slope of the perpendicular line is:
n = -1/m
This gives
n = -1/0.5
n = -2
The equation is then calculated as:
y = n(x - x1) + y1
This gives
y = -2(x - 1) + 2
Expand
y = -2x + 2 + 2
Evaluate
y = -2x + 4
Hence, the equation of the perpendicular line is y = -2x + 4
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Which answer choice shows that the set of irrational numbers is not closed under addition? π+(-π)=0
1/2+(-1/2)=0
π+π=2π
1/2+1/2=1
Answers
Answer:
(a) π + (-π) = 0
Step-by-step explanation:
You want a counterexample for the statement that irrationals are closed under addition.
Closed setA set is closed under addition if adding members of the set always results in a member of the set.
π + (-π) = 0This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.
(1/2) + (-1/2) = 0Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
π + π = 2πAn example of a sum that is an element of the set. This is not a counterexample.
(1/2) +(1/2) = 1Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
<95141404393>
GIVING BRAINIEST ITS DUE IN 32 MINS !!!
Answers
\( \bf \large \implies{6.5}\)
Step-by-step explanation:As shown in the figure, in the 40 games,
\( \bf{(3 + 6 + 4) = 13 \: ahead}\)
\( \bf{p \: = \: \frac{13}{40} }\)
\( \bf{So \: N = 20 \times p \: = 20 \times \frac{13}{40} = 6.5}\)
In the 20 games, the team will be ahead in atleast one of the halves in 10.5 games.
We can see in the given data that the number of halves which ended in atleast one ahead is 3 + 6+ 4 + 5 + 3 = 21
Hence, the probability of getting ahead is 21/40.
We have to find the number of games in which the team will get ahead in atleast one of the halves in the next 20 halves according to the given data.
Hence, the number of games in which the team will get ahead in atleast one of the halves in the next 20 halves is 20*(21/40) = 21/2 = 10.5 games.
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A picture of a bridge in the country of Croatia is shown below
Which type of angle best describes /_ACB?
A. acute
B. right
C. obtuse
D. straight
Answers
When the student gets home, she gives 1/2 of her remaining fudge to her sister.
How many ounces of fudge does she give her sister?
Answers
The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces
What is a fraction?A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.
Part of the question obtained from a similar question posted online can be presented as follows;
The amount of fudge the student has = 3 pounds
The amount of fudge the student eats = 1 pound of the fudge
Required; The amount of fudge the student has left
The amount of fudge the student has left = 3 - 1 = 2 pounds
The fraction of the remaining fudge the student gives to her sister = (1/2)
Therefore;
The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound
1 pound = 16 ounces
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Put the correct punctuation after each sentence.
What is your name
Help me
I love my family
No, Denise
How old are you__
My dog is small
Look up in the sky.
Go to bed
I can read
Do you want to play_
I love school
The house is on fire
I am happy_
Where are we going
Log
Answers
2 ! or .
3. .
4. ! or .
5. ?
6. .
7. .
8. !
9. .
10. ?
11. !
12.! or .
13. ?
What is the value of the digit in the ones place?
2,615
A. 50
B. 5
OC. 2,000
OD. 100
Answers
Need help on this one, can someone please answer this?
Answers
Answer:
quadrant 3
Step-by-step explanation:
It takes Cindy about 30 minutes to paint a picture.
About how long would it take Cindy to paint 2 pictures?
Answers
Answer:
60 mins
Step-by-step explanation:
1 picture = 30 mins
times both sides by 2 to get 2 pictures
2 pictures = 60 mins
Answer:
what are coprime number
x = -3.
3.2 2 - 16=(x-1)=?
Answers
Answer:
dvide it
Step-by-step explanation:
Please answer this question.
Answers
Answer:
Step-by-step explanation:
\(1c-0.25c=0.75c\)