SOLUTION: Liam recently graduated from USF and accepted a job as a software engineer. The starting salary is $75,000 and has a guaranteed annual pay increase of 3% each year. The equation m

Algebra ->  Finance -> SOLUTION: Liam recently graduated from USF and accepted a job as a software engineer. The starting salary is $75,000 and has a guaranteed annual pay increase of 3% each year. The equation m      Log On


   

Question 1206479: Liam recently graduated from USF and accepted a job as a software engineer.
The starting salary is $75,000 and has a guaranteed annual pay increase of 3% each year. The equation models the increase in salary over time, where x is the number of years since he started at the company and y is his salary.
a) Describe how to determine whether the situation models exponential growth or decay.
b) What does the y-intercept represent in this situation?
c) If Liam works for the company for 30 years, determine the domain and range.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
starting salary is 75000
salary increases by 3% per year
formula becomes y = 1.03 ^ x
each year he makes 3% more than he made the last year.

it is exponential growth because the growth factor is greater then 1.

if it was exponential decay, the growth factor would have been greater than 1.

the y-intercept represents his starting salary of 75,000.

that's the value of y when x is 0.

if he works for the company for 30 years, the domain would be the value of x from 0 to 30 and the range would be the value of y for x = 1 to 30.

the equation can be graphed as shown below.

the growth factor is 1 plus the growth rate.

if there is growth, the growth rate is positive and the growth factor is greater than 1.

if there is decay, the growth rate is negative and the growth factor is less than 1.

for example:

3% growth rate gets you a growth factor of 1 + .03 = 1.03 which is greater than 1.

-3% growth rate gets you a growth factor of 1 - .03 = .97 which is less than 1.

the first graph below shows a positive growth rate of 3% per year.
this give you a growth factor greater than 1.

the second graph below shows a negative growth rate of 3% per year.
this gives you a growth factor less than 1.