A six-year old house, now worth $$175,000$, has had an annual appreciation of $5$%.  

1. What is the multiplier?

   Hint (a):

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

2. What did it cost when 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 $f(t) = ab^t$, where t is the time in years, that represents the value of the house since it was new.

   Answer (c):

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