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Calculus IChapter 1: ReviewSection 1-7

Exponential Functions — Question 7

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Question 7

The number of viewers watching a viral video on a social media platform can be modeled by the function V(t)=1500⋅e0.7tV(t) = 1500 \cdot e^{0.7t} where V(t)V(t) is the number of viewers and tt is the time in days since the video was posted.

  • (a) How many people have viewed the video after 2 days?

  • (b) After how many days will the video have 50,000 viewers?

  • (c) What is the average rate of change of viewers between day 1 and day 3?

Round all answers to two decimal places.

Original worksheet page 1: question and worked solution for 1-7-007
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Question 7 - Solution

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

(a)

V(2)=1500e1.4V(2)=1500e^{1.4}

6082.80viewers\boxed{6082.80\quad\text{viewers}}

(b)

t=ln⁡(50000/1500)/0.7t=\ln(50000/1500)/0.7

5.01days\boxed{5.01\quad\text{days}}

(c)

V(3)−V(1)3−1=750(e2.1−e0.7)\dfrac{V(3)-V(1)}{3-1}=750(e^{2.1}-e^{0.7})

4614.31viewers/day\boxed{4614.31\quad\text{viewers/day}}

Original worksheet page 2: question and worked solution for 1-7-007

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