## Exponential and Logarithm Functions in Finance

Many applications in business are based upon a rate of growth or decay given as a percentage. For instance, the rate at which the value of a $150,000 home is increasing may be given as 2% per year. The value of the home t years later would be

Other quantities will decrease by a percentage. At the completion of a marketing campaign, sales for a new tablet computer are 550,000. Sales decrease by 5 percent per week from that point onward. The sales* t* weeks later may be modeled by

Each of these quantities are modeled by an exponential function of the form

where *a* is the original amount of the quantity and *r* is the rate in percent per time. The time should correspond to the units of time on the variable *t*. The plus sign is used when the function is an increasing exponential function. The minus sign is used when the quantity is decreasing.

In this section, you’ll learn how to use logarithms to solve equations arising from exponential functions.

**Read **in Section 5.2

- How do you convert between the exponential and logarithmic forms of an equation?
- How do you evaluate a logarithm?
- How do you solve problems using logarithms?

**Watch **Video

## Applications

- Handout: Exponential Sales