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).