Question

3 of the answers are not correct.
your starting salary at a company is 60000 dollars, and you get a raise of 3000 dollars each year. let t represent the number of years since you joined the company.
a) express the percentage rate of change of your salary as a function of time.
r(t) = 2000
b) at what percentage rate will your salary be increasing after 2 years?
the percentage rate your salary will be increasing is 200 %
c) what value does the percentage rate of change of your salary approach in the long run?
10 %

Explanation:

Step1: Define salary function

Let \( S(t) \) be salary at year \( t \).
\( S(t) = 60000 + 3000t \)

Step2: Find percentage rate function

Percentage rate \( r(t) = \frac{\text{Annual raise}}{\text{Current salary}} \times 100\% \)
\( r(t) = \frac{3000}{60000 + 3000t} \times 100\% = \frac{100}{20 + t}\% \)

Step3: Calculate rate at t=2

Substitute \( t=2 \) into \( r(t) \)
\( r(2) = \frac{100}{20 + 2}\% = \frac{100}{22}\% \approx 4.55\% \)

Step4: Find long-run limit

Take limit as \( t \to \infty \)
\( \lim_{t \to \infty} \frac{100}{20 + t}\% = 0\% \)

Answer:

a) \( r(t) = \frac{100}{20 + t}\% \)
b) \( \approx 4.55\% \)
c) \( 0\% \)