Final answer:
The derivative (dA)/(dt) of the function A(t) = 2000e^{0.005t} with respect to time t is 10e^{0.005t}. This is found by applying the differentiation rules for exponential functions directly to A(t).
Step-by-step explanation:
The student has provided the function A(t) = 2000e^{0.005t} which describes some quantity A as a function of time. To find the derivative of A with respect to time, (dA)/(dt), we will use the rules of differentiation for exponential functions.
We start by differentiating A(t) with respect to t:
d/dt[2000e^{0.005t}] = 2000 * d/dt[e^{0.005t}]
The derivative of e^{kt} with respect to t is ke^{kt}, where k is a constant. Thus, the derivative of e^{0.005t} with respect to t is 0.005e^{0.005t}:
(dA)/(dt) = 2000 * 0.005e^{0.005t}
This simplifies to:
(dA)/(dt) = 10e^{0.005t}