Question

Catherne ts considering job offers ffom two cempanics. Company A otiered her a starting salary of $52,000 with a $2100 raise at the end of each year. Company B offered ber a starting salafy of $52,000 with a 4.4% raise at the end of each year. Let a(t) represent Catherind's salary at Compaby A t yearn after accepting a position at Company A, and let O(t) reptesent Cat lerine's salary at Company B t years after accepting a position at Company

Answer 1

Catherine's offers from Company A and Company B represent linear and exponential salary growth respectively. Company A offers a fixed annual raise while Company B offers a percentage-based raise. To compare, one can use the respective formulas for each company and calculate for different years.

Step-by-step explanation:

Catherine is evaluating job offers that have different salary growth rates. For Company A, the salary growth is linear, because she gets a fixed raise every year. For Company B, the salary growth is exponential, because she gets a percentage-based raise every year. To compare these, we can use the formulas for linear and exponential functions respectively.

For Company A, a(t) = 52000 + 2100t, where t is the number of years at the company.

For Company B, b(t) = 52000(1 + 0.044)^t, which represents a 4.4% raise compounded annually.

To determine which company offers the better salary in the long term, she would need to evaluate these formulas for different values of t and compare.