Question

a plumber is hired with an annual salary of $55,000. the function a(t) = 55,000 - (1.14)^t models the annual salary, a(t), in dollars, for a given number of years. part a: find the percent rate of change. show all necessary steps. (5 points) part b: explain the meaning of the percent rate of change in the context of the problem. (5 points)

Explanation:

Step1: Identify growth - factor form

The general form of an exponential growth function is $a(t)=a_0(1 + r)^t$, where $r$ is the rate of change. Here $a(t)=55000\times(1.14)^t$, so $1 + r=1.14$.

Step2: Solve for $r$

$r = 1.14-1=0.14$. As a percentage, $r = 14\%$.

Answer:

Part A: 14%
Part B: The plumber's salary increases by 14% each year.