Below are two situations that can be described using exponential functions. They represent a small sampling of the situations where quantities grow or decay by a constant percentage over equal periods of time. For each situation:

• Find an appropriate unit of time (such as days, weeks, years).

• Find the multiplier that should be used.

• Identify the initial value.

• Write an exponential equation in the form $f(x)=ab^x$ that represents the growth or decay.

1. A house purchased for $\$120,000$ has an annual appreciation of $6\%$.

   Answer (a):

   Years; $1.06;120,000$

   $f(x)=120000(1.06)^{x}$

2. The number of bacteria present in a colony is $180$ at noon, and it increases at a rate of $22\%$ per hour.

   Hint (b):

   This problem is similar to part (a) above.