# Thread: Log Word Problem #1

1. ## Log Word Problem #1

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?

2. Originally Posted by skeske1234
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?
Firm A represents a constant rise rather than the exponential rise you have described:

$A = 40000 + 2000t = 2000(20+t)$

Firm B is more ambiguous because it does not say whether the 5% is compounded. Here I have said that it is compounded and arrive at the same equation as you.

$B = 38500(1+0.05)^t$

To solve part 2 make them equal and solve for t. Since you have an exponential and a linear term it's likely a numerical approximation is needed