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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 An educational technologist is analyzing video content engagement. A video on algebraic geometry receives views according to the function \( V(t) = 200e^{0.05t} \), where \( V(t) \) is the number of views after \( t \) days. How many views does the video receive in the first 10 days?

📌 Calculate the total views over 10 days by evaluating the definite integral of \( V(t) \) from 0 to 10:

📌 \text{Total views} = \int_0^{10} 200e^{0.05t} \, dt

📌 The antiderivative of \( 200e^{0.05t} \) is:

📌 \frac{200}{0.05} e^{0.05t} = 4000e^{0.05t}

📌 Evaluate at the bounds:

📌 4000e^{0.5} - 4000e^{0} = 4000(e^{0.5} - 1)

📌 Approximate \( e^{0.5} \approx 1.64872 \):

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