STEM-Master
Calculus IChapter 1: ReviewSection 1-7

Exponential Functions — Question 5

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Question 5

A scientist is growing a bacteria culture in a lab. The population of bacteria at time tt hours is given by the function: P(t)=1200e0.55tP(t) = 1200e^{0.55t}

  • (a) What is the population after 4 hours?

  • (b) After how many hours will the population reach 10,000?

  • (c) By what percentage does the population increase each hour?

Round all answers to two decimal places.

Original worksheet page 1: question and worked solution for 1-7-005
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Question 5 - Solution

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

(a)

P(4)=1200e2.2P(4)=1200e^{2.2}

10830.02bacteria\boxed{10830.02\quad\text{bacteria}}

(b)

t=ln⁡(10000/1200)/0.55t=\ln(10000/1200)/0.55

3.86hours\boxed{3.86\quad\text{hours}}

(c)

100(P(t+1)/P(t)−1)=100(e0.55−1)100(P(t+1)/P(t)-1)=100(e^{0.55}-1)

73.33%\boxed{73.33\quad\text{\%}}

Original worksheet page 2: question and worked solution for 1-7-005

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