A2.A.6Solve an Application Which Results in an Exponential Function

Name ______Date ______

Algebra II & TrigonometryExponential Functions

A2.A.6Solve an application which results in an exponential function

A2.A.12Evaluate exponential expressions, including those with base e

1. The following formulas represent salaries promised to new employees at five different software companies, where t represents years.

i. P(t) = 38,500 + 1,000t

ii. P(t) = 35,000(1.062)t

P(t) = 32,000(1.5)t
P(t) = 41,000
P(t) = 47,500 – 1500t

Match the four following statements with the salaries shown above.

This company promises a constant salary, no raises.

The company offers a $1000 bonus for each year of service.

An employee who stayed with this company for 2 years would more than double her salary.

If an employee stayed with this company long enough, she would end up paying the company to work there.

Now write a description of the salary function you did not use in the matching.

2. The population of the village of Elfdom in the North Pole suburbs has a steady population represented by the exponential function P(t) = 11,493 (1.029587)t, where t represents the number of years since 1985 when the village was incorporated.

(a) What is the annual rate of growth?

(b) In what calendar year will the population be 17,500?

3. Each time Juanita bowls, her score increases by 5% of her previous score. If her initial score is represented by a, write an equation that shows this relationship.

4. Sean and Liz graduate from college in the same year and start working at different firms. Sean’s salary, in thousands of dollars, is represented by the exponential function H(t) = 39.5(1.045)t, while Liz’s salary, in thousands of dollars, is represented by the exponential formula E(t) = 34.6(1.054)t.

(a) Whose salary is higher when the pair start working? What is each salary?

(b) Describe the behavior of the two formulas and interpret their meaning.