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2-19.

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

• ​What is an appropriate unit of time (such as days, weeks, years)?

• What is the multiplier that should be used?

• What is the initial value?

• Write the equation of an exponential function that represents the situation.

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

Time is in years.

The multiplier is $1.0+6\%$.

$f(x)=120,000(1.06)^x$

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

Use the same method as (a).