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Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views
t days after Nora uploaded the video:

V(t)=100*e^(0.4 t)
What is the instantaneous rate of change of the number of views 4 days after the video was uploaded?
Choose 1 answer:
(A) 198 views
(B) 198 views per day
(C) 495 views
(D) 495 views per day

Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views $t$ days after Nora uploaded the video: $\newline$ $V(t)=100 \cdot e^{0.4 t}$ $\newline$ What is the instantaneous rate of change of the number of views $4$ days after the video was uploaded? $\newline$ Choose $1$ answer: $\newline$ (A) $198$ views $\newline$ (B) $198$ views per day $\newline$ (C) $495$ views $\newline$ (D) $495$ views per day

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views

t

days after Nora uploaded the video:

\newline

V(t)=100 \cdot e^{0.4 t}

\newline

What is the instantaneous rate of change of the number of views

4

days after the video was uploaded?

\newline

Choose

1

answer:

\newline

(A)

198

views

\newline

(B)

198

views per day

\newline

(C)

495

views

\newline

(D)

495

views per day

Take Derivative of $V(t)$ : To find the instantaneous rate of change, we need to take the derivative of $V(t)$ with respect to $t$ .
$V(t) = 100 \cdot e^{0.4t}$
$\frac{dV}{dt} = 100 \cdot 0.4 \cdot e^{0.4t}$
Evaluate at $t = 4$ : Now we need to evaluate the derivative at $t = 4$ days. $\frac{dV}{dt} = 100 \times 0.4 \times e^{(0.4\times4)}$
Simplify the Expression: Simplify the expression. $\frac{dV}{dt} = 40 \cdot e^{1.6}$
Calculate $e^{1.6}$ : Use a calculator to find the value of $e^{1.6}$ . $\newline$ $e^{1.6} \approx 4.953$ (rounded to three decimal places)
Multiply by $40$ : Multiply $40$ by the value of $e^{1.6}$ . $\newline$ $\frac{dV}{dt} = 40 \times 4.953$

More problems from Volume of cubes and rectangular prisms: word problems

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Chinedu was given this problem:

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Question

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Question

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Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant