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?

   Hint (a):

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

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

   Hint (b):

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

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

   Answer (c):

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