Question

A=3500(1.03)^t what is the rate of change per time period? please explain

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change per time period, we need to find the derivative of the given function A(t) with respect to t.

Given A(t) = 3500(1.03)^t, we can find the derivative by using the chain rule:

dA/dt = 3500 * ln(1.03) * (1.03)^t = 3500 * ln(1.03) * (1.03)^t

The rate of change per time period is the derivative of the function, which gives us the instantaneous rate of change of the function with respect to time.

Therefore, the rate of change per time period is equal to 3500 * ln(1.03) * (1.03)^t.

Answer 2

that is an increase of 3% each time period

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, that is correct. The rate of change per time period is the derivative of the function, which in this case is equal to 3500 * ln(1.03) * (1.03)^t.

Since the function A(t) = 3500(1.03)^t represents exponential growth with a factor of 1.03 (or an increase of 3%) per time period, the rate of change per time period is indeed an increase of 3% each time period. Thank you for pointing that out.