Advanced Functions

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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 -

    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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