Posted by **please help!** on Sunday, December 13, 2009 at 10:26pm.

Rena has been offered entry-level positions with two firms.

Firm A offers a starting salary of $40 000 per year, with a $2000 per year increase guaranteed each subsequent year.

Firm B offers a starting salary of $38 500, with a 5% increase every year after that.

a)After how many years will Rena earn the same amount at each firm?

b) At which firm will Rena earn more after

i) 10 years ii) 20 years

- Advanced Functions -
**Reiny**, Sunday, December 13, 2009 at 10:41pm
Firm A's salaries increase linearly, (they form an arithmetic sequence)

Firm B;s salaries increase exponentially, (they form a geometric sequence)

SA = 2000t + 40000, where t is number of years after starting

SB = 38500(1.05)^t

a) you would have to solve

38500(1.05^t = 40000 + 2000t

385(1.05)^t = 400 + 20t

I would just try a few values of t

t Left-side RS

5 491 500

8 569 560

7 542 540

9 597 580

What is your conclusion?

for b) just sub t = 10 and t = 20 into both equations.

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