# Logarithm Function

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Chels is a recent business grad and 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 38500, with a 5% increase every year after that.

a) after how many years will Renata earn the same amount at either firm?

b) what other factors might affect Chels's choice, such as opportunities for promotion? Explain how these factors may influence her decision.

So my attempt at question a) is like this:

40,000(2000)^t = A(t) for firm A
38,500(1.05)^t = A(t) for firm B

Is this wrong or right and could you provide me with the correct equation if this is wrong as well?

• Logarithm Function -

no
although I would love to have the salary stated by your
a(t) = 40,000(2000)^t

the offer from Firm A is an arithmetic sequence, while Firm B's plan is a geometric sequence
your equation for the second offer is correct

Plan A would be
A(t) = 40000 + 2000t

so you are solving
38000(1.05)^t = 40000 + 2000t

after a few trial and error substitutions I got

t = 7, LS = 54173, RS = 54000
t = 8, RS = 56882, RS = 56000

so between 7 and 8 years time, the two offers would be the same.

• Logarithm Function -

t = 6, LS = 51593, RS = 52000

so the salaries are about equal between 6 and 7 years.

ignore the previous conclusion

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