Question

A math teacher gets a starting salary of $30,000. IF she gets a 1.5% increase in salary each year, what will her total income be over a thirty year period?

This was a past mathlete problem.
I know we have to use an exponential function, but do I have to use the base e? Or should I just do a base of 1.015?

Answer 1

No it is not base e. It is 1.015.

An increase of 1.5 % = 1.015

Year 1, 2, 3,.........................., 30.
30000, 3000(1.015), 30000(1.015)²,........... 30000(1.015)²⁹

Her Total Income is sum over the thirty 30 year period:

Sn = a(r^n - 1) / (r - 1); a = 30000, r = 1.015, n = 30

Sn = 30000 ( 1.015^30 - 1) / (1.015 - 1)

= 30000 (1.56308022 - 1) / (0.015) = 1126160.44

Total = $ 1 126 160.44