The exponential function that gives the dollar value (v) of a certain house that is t years old is:
v(t) = 427,500(1.08)^t
This function is of the form:
v(t) = a(b)^t
where a = 427,500 and b = 1.08.
The value of a represents the initial value of v, which is the value of the house when it is zero years old. In this case, a = 427,500 represents the initial value of the house when it is brand new.
The value of b represents the growth factor of v, which is the factor by which v increases each year. In this case, b = 1.08 represents a 8% annual increase in the value of the house.
To find the value of the house when it is 10 years old, we can substitute t = 10 into the function:
v(10) = 427,500(1.08)^10
Using a calculator, we can evaluate this expression:
v(10) ≈ $977,684.11
Therefore, the value of the house when it is 10 years old is approximately $977,684.11.