Question

g(t)= 200(1.12)^t For each function below, enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.

Answer 1

Percent rate of change per unit, t ≈ 10.99%

Explanation:

The percent rate of change per unit, t, for a function is equal to the derivative of the function with respect to t, divided by the function value at t.

For the given function g(t) = 200(1.12)^t, the derivative with respect to t is:

g'(t) = ln(1.12) * 200(1.12)^t

The function value at t is:

g(t) = 200(1.12)^t

Therefore, the percent rate of change per unit, t, is:

g'(t) / g(t) = [ln(1.12) * 200(1.12)^t] / [200(1.12)^t] = ln(1.12) ≈ 0.1099

Multiplying by 100 to express the answer as a percentage, rounded to the nearest tenth of a percent, we get:

Percent rate of change per unit, t ≈ 10.99%