2.06 Applications of Exponential Functions

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2.06 Applications of Exponential Functions

State whether each function represents an Exponential Growth or Decay model and calculate the percent rate of change (written as a percent). Show all work.

1. / f(x) = 2(3.9)x / Exponential Growth/Decay: / Percent Rate of Change: %
Show work here:
2. / g(x) = 4.6(0.23)x / Exponential Growth/Decay: / Percent Rate of Change: %
Show work here:
3. / f(x) = 3.4(0.95)x / Exponential Growth/Decay: / Percent Rate of Change: %
Show work here:
4. / f(x) = −4(1.2)x / Exponential Growth/Decay: / Percent Rate of Change: %
Show work here:

A new home was purchased for $256,000 and the value of the home appreciates by 1.3% per year. Use this information to answer questions 5 – 7.Round any decimals to at least two decimal values.

5. / Calculate the value of the home after 8 years.
Exponential Growth/Decay: / a = / r = / x =
Show work here:
The value of the home after 8 years is $.
6. / Calculate the value of the home after 8 years if it depreciated by 0.6% per year.
Exponential Growth/Decay: / a = / r = / x =
Show work here:
The value of the home after 8 years of depreciation will be $.
7. / A typical mortgage (house payments) is 30 years. Determine if the home would have doubled in value half-way through the payments (after 15 years).
Exponential Growth/Decay: / a = / r = / x =
Show work here:
The value of the home after 15 years of appreciation will be $. The value (will/will not) have doubled half-way through the mortgage.

You are shopping for a new car. You have two options for your new car which are listed below.

Option A: Original cost of the car is $16,500 and depreciates 6% per year.

Option B: Original cost of the car is $20,500 and depreciates 8% per year.

After eight years, determine the value of each car.

8. / Value of Option A = / $ / Value of Option B = / $
Show work here: / Show work here:
9. / After 8 years, which car has the highest value?