Question

The function $P(t) = 4.4e^{0.15t}$ takes t, days since an algal culture was prepared, and gives A, area covered by the culture (in square centimeters). Determine the derivative $P'(t)$ and then use it to calculate $P'(7)$, which gives the rate of growth of the culture on day 7 (in square centimeters per day). Your answer needs to be accurate to two decimal places. Answer

Name: the function pt 44e015t takes t days since an algal culture was prepared and gives a area covered by the culture in square centimeters determine the derivative pt and then use it to calculat 33936
Uploaded: 2022-11-21T23:14:58-08:00
Duration: 3 min 12 s
Channel: Carson Merrill
Description: the function pt 44e015t takes t days since an algal culture was prepared and gives a area covered by the culture in square centimeters determine the derivative pt and then use it to calculat 33936

          The function $P(t) = 4.4e^{0.15t}$ takes t, days since an algal culture was prepared, and gives A, area covered by the culture (in square centimeters). Determine the derivative $P'(t)$ and then use it to calculate $P'(7)$, which gives the rate of growth of the culture on day 7 (in square centimeters per day). Your answer needs to be accurate to two decimal places.

Answer

the function pt 44e015t takes t days since an algal culture was prepared and gives a area covered by the culture in square centimeters determine the derivative pt and then use it to calculat 33936

Added by Mackenzie M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

11/21/2022

Step 1

4e^{0.15t}$. We need to find the derivative $P'(t)$. Using the chain rule for differentiation, if $f(x) = ce^{kx}$, then $f'(x) = cke^{kx}$. In our case, $c = 4.4$ and $k = 0.15$. So, $P'(t) = 4.4 \times 0.15 \times e^{0.15t}$. $P'(t) = 0.66e^{0.15t}$. Show more…

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The function $P(t) = 4.4e^{0.15t}$ takes t, days since an algal culture was prepared, and gives A, area covered by the culture (in square centimeters). Determine the derivative $P'(t)$ and then use it to calculate $P'(7)$, which gives the rate of growth of the culture on day 7 (in square centimeters per day). Your answer needs to be accurate to two decimal places. Answer