### Home > INT2 > Chapter 11 > Lesson 11.2.2 > Problem11-73

11-73.

A six‑year old house, now worth $175{,}000$, appreciates at an annual rate of $5\%$.

1. If you want to calculate the value of the house at a given time, what is the multiplier you need to use in this situation?

Because the house value is appreciating, the multiplier must be greater than $1$.

1. What did the house cost when it was new?

Substitute the information in the problem into the generic exponential function.
Then calculate backwards to find the original value.

2. Write a function of the form $f(t) = ab^t$ that represents the value of the house $t$ years after it was first built.

$f(t) = 130588(1.05)^t$