To find the instantaneous rate of change at 5 years, we need to find the derivative of the given function with respect to x and then evaluate it at x=5.
Given function: f(x) = 130000(1.06)^x
Taking the derivative of f(x) with respect to x:
f'(x) = d/dx [130000(1.06)^x]
f'(x) = 130000 * (1.06)^x * ln(1.06)
Evaluating f'(5):
f'(5) = 130000 * (1.06)^5 * ln(1.06)
f'(5) ≈ 130000 * 1.338225 * 0.058269 = 10022.69
Therefore, the best estimate for the instantaneous rate of change in the value of the home when the family owned it for 5 years is approximately $10,022.69 per year.
The value of a family's home is given by (X) = 130 000(1. 06)x
, where x
is a the number of years after the family purchases the house for $130 000. What is the best estimate for the instantaneous rate of change in the value of the home when the family owned it for 5 years?
1 answer