Question

After finishing her management degree, Jenny started a job with a fixed percentage for an annual raise. Jenny’s annual salary is modeled by the equation A = 100,000(1.065)t where t represents the years she’s been working for the company. Her friend Donald graduated from the same college and started a different job. His annual salary is modeled by the equation A = 85,000(1.07)t.

Answer 1

With that information, assuming both Jenny and Donald started to work at the same time, you can calculate when the salary of Donald will match or exceed Jenny's salary.

For that, you equal both expressions:

Jenny's salary = Donald's salary

100,000 (1.065)ⁿ = 85,000 (1.07)ⁿ

Note that I am using n only for facilities of the editor. You use t in your work.

⇒ 1.07ⁿ = (100/85) (1.065)ⁿ

(1.07 / 1.065)ⁿ = (100/85)

n log [ 1.07/1.065] = log (100/85)

n = log (1.1765) / log (1.0108) = 0.0706 / 0.00466 = 15

That means that after 15 years Donald's salary will match Jenny's salary