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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 t days after Nora uploaded the video:\newlineV(t)=100⋅e0.4t V(t)=100 \cdot e^{0.4 t} \newlineWhat is the instantaneous rate of change of the number of views 44 days after the video was uploaded?\newlineChoose 11 answer:\newline(A) 198198 views\newline(B) 198198 views per day\newline(C) 495495 views\newline(D) 495495 views per day

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Q. Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views t t days after Nora uploaded the video:\newlineV(t)=100⋅e0.4t V(t)=100 \cdot e^{0.4 t} \newlineWhat is the instantaneous rate of change of the number of views 44 days after the video was uploaded?\newlineChoose 11 answer:\newline(A) 198198 views\newline(B) 198198 views per day\newline(C) 495495 views\newline(D) 495495 views per day
  1. Take Derivative of V(t)V(t): To find the instantaneous rate of change, we need to take the derivative of V(t)V(t) with respect to tt.
    V(t)=100⋅e0.4tV(t) = 100 \cdot e^{0.4t}
    dVdt=100⋅0.4⋅e0.4t\frac{dV}{dt} = 100 \cdot 0.4 \cdot e^{0.4t}
  2. Evaluate at t=4t = 4: Now we need to evaluate the derivative at t=4t = 4 days.dVdt=100×0.4×e(0.4×4)\frac{dV}{dt} = 100 \times 0.4 \times e^{(0.4\times4)}
  3. Simplify the Expression: Simplify the expression. dVdt=40⋅e1.6\frac{dV}{dt} = 40 \cdot e^{1.6}
  4. Calculate e1.6e^{1.6}: Use a calculator to find the value of e1.6e^{1.6}.\newlinee1.6≈4.953e^{1.6} \approx 4.953 (rounded to three decimal places)
  5. Multiply by 4040: Multiply 4040 by the value of e1.6e^{1.6}. \newlinedVdt=40×4.953\frac{dV}{dt} = 40 \times 4.953

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