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\( P = 500 \cdot 2.4760 = 1,238 \)
#### 1,238
A calculus communicator models the spread of a viral video: \( V(t) = 1000 \cdot e^{0.4t} \), where \( t \) is in days. Find the rate of change of views at \( t = 3 \) days.
Rate of change is \( V'(t) = 1000 \cdot 0.4 \cdot e^{0.4t} = 400 \cdot e^{0.4t} \)
At \( t = 3 \): \( V'(3) = 400 \cdot e^{1.2} \)
\( e^{1.2} \approx 3.3201 \)
\( V'(3) = 400 \times 3.3201 = 1,328.04 \) views per day
#### 1,328.04
A Netflix recommendation system uses a logistic growth model for viewership: \( U(t) = \frac{10,000}{1 + 9e^{-0.5t}} \). Find the viewership after 4 days.
\( U(4) = \frac{10,000}{1 + 9e^{-0.5 \cdot 4}} = \frac{10,000}{1 + 9e^{-2}} \)