Asked by Thank you so much 😊
A=3500(1.03)^t what is the rate of change per time period? please explain
Answers
Answered by
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.
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.
Answered by
oobleck
that is an increase of 3% each time period
Answered by
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.
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.