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Find the growth rate of P=15e^(.067t)

User Winfield
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To find the growth rate of the function P = 15e^(0.067t), we differentiated the function with respect to time (t) using the chain rule. The growth rate is given by the derivative dP/dt = 1.0055e^(0.067t).

To find the growth rate of the function P = 15e^(0.067t), we need to differentiate the function with respect to time (t).

Given: P = 15e^(0.067t)

To differentiate e^(0.067t), we use the chain rule. The derivative of e^(kt) with respect to t is ke^(kt). In this case, k = 0.067, so the derivative of e^(0.067t) is 0.067e^(0.067t).

Now, let's differentiate the function P = 15e^(0.067t):

dP/dt = d(15e^(0.067t))/dt

= 15 * d(e^(0.067t))/dt

= 15 * 0.067e^(0.067t)

Simplifying further, we have:

dP/dt = 1.0055e^(0.067t)

Therefore, the growth rate of the function P = 15e^(0.067t) is given by dP/dt = 1.0055e^(0.067t).

User Monotux
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