STEM-Master
Calculus IChapter 1: ReviewSection 1-7

Exponential Functions — Question 1

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Question 1

The population of a bacterial culture is modeled by the function P(t)=500e0.3tP(t) = 500e^{0.3t} where tt is measured in hours.

  • (a) What is the population after 5 hours?

  • (b) After how many hours will the population reach 3000?

  • (c) By what factor does the population grow every 4 hours?

Round your answers to two decimal places.

Original worksheet page 1: question and worked solution for 1-7-001
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Question 1 - Solution

Use the exact exponential model and keep full precision until the final rounding.

(a)

P(5)=500e1.5P(5)=500e^{1.5}

2240.84bacteria\boxed{2240.84\quad\text{bacteria}}

(b)

500e0.3t=3000⇒t=ln⁡(6)/0.3500e^{0.3t}=3000\ \Longrightarrow\ t=\ln(6)/0.3

5.97hours\boxed{5.97\quad\text{hours}}

(c)

P(t+4)/P(t)=e1.2P(t+4)/P(t)=e^{1.2}

3.32growth factor\boxed{3.32\quad\text{growth factor}}

Original worksheet page 2: question and worked solution for 1-7-001

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