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DochEvi [55]
1 year ago
7

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a

relative rate of 3% per hour. Suppose that a sample culture has an initial population of 428 bacteria. Find the predicted population after six hours. Do not round any intermediate computations, and round your answer to the nearest tenth.
Mathematics
1 answer:
damaskus [11]1 year ago
4 0

The predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to <u>512.4</u> bacteria in 6 hours.

A continuous exponential growth model is used to determine the final value of a quantity (V), from an initial value of the quantity (V₀), at a rate of continuous growth per unit time (r), after the time (t), as:

V = V_0e^{rt}.

In the question, we are given that the number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 3% per hour.

We are asked, to find the predicted population after six hours when the initial population was 428 bacteria.

Thus, we take V₀ = 428, r = 3% = 0.03, and t = 6, in the equation:

V = V_0e^{rt} ,

to find the predicted population (V) of bacteria after 6 hours.

Thus,

V = 428e^{0.03*6}\\\Rightarrow V = 428e^{0.18}\\\Rightarrow V = 428*1.1972173631218\\\Rightarrow V = 512.40903141613\\\Rightarrow V = 512.4

Rounding to the nearest tenth.

Thus, the predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to <u>512.4</u> bacteria in 6 hours.

Learn more about the continuous exponential growth model at

brainly.com/question/9235073

#SPJ4

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Nastasia [14]

\huge \boxed{\mathbb{QUESTION} \downarrow}

  • Revathi's age is 1/3 of her mother's age. If their difference in age is 24 years, find Revathi's age.

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

Given,

  • Mother's age = x
  • Revathi's age = 1/3 x = ?
  • Difference in their age = 24 years ⇨ x - 1/3 x = 24.

Now, let's solve this question using the above equation which we just formed.

\sf \: x -  \frac{1}{3}x  = 24 \\

Combine x and \sf\:-\frac{1}{3}x to get \sf\frac{2}{3}x.

\sf\frac{2}{3}x=24  \\

Multiply both sides by \sf\frac{3}{2}, the reciprocal of \sf\frac{2}{3}.

\sf \: x=24\times \left(\frac{3}{2}\right)

Express \sf24\times \left(\frac{3}{2}\right) as a single fraction.

\sf \: x=\frac{24\times 3}{2}  \\

Multiply 24 and 3 to get 72.

\sf \: x=\frac{72}{2}  \\

Divide 72 by 2 to get 36.

\boxed{ \bf \: x=36 }

We now have the age of Revathi's mother (x) = <u>36 years</u>. Now, let's find Revathi's age ⇨ \sf\:(\frac{1}{3}x)

\rightarrow \sf \:  \frac{1}{3} x  \\  \rightarrow \sf \: \frac{1}{3}  \times 36 \\  \rightarrow \sf \: \frac{1}{ \bcancel  3}  \times  \bcancel{36} \\  \rightarrow \sf \:1 \times 12 \\  =    \boxed{\boxed{\bf \: 12}}

  • So, Revathi is <em><u>1</u></em><em><u>2</u></em><em><u> </u></em><em><u>years </u></em><em><u>old.</u></em>
6 0
3 years ago
Read 2 more answers
if it’s possible could anyone do atleast question 11, 13, and 16 for me? so i can understand how to do them! sorry if it’s a lot
liq [111]
11) 7
13) 3/40
16) 9/4
5 0
3 years ago
3x−1=1−3x. Needs to be in simpilest form.
xz_007 [3.2K]

Answer:

x= 2/6

Step-by-step explanation:

add 3x to both sides

add 1 to both sides

divide 6 to both sides to isolate x

x = 2/6

8 0
3 years ago
Is -7-5+3=1 true or false
grigory [225]
-7-5+3=1
-12+3=1
-9≠1. As a result, this is False. Hope it help!
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Lisa is on a trip of 887 miles. She has already traveled 98 miles. She has 3 days left in her trip. How many miles does she need
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