The amount to which $100 will grow in t years with an interest rate (r) compounded annually is given by the polynomial function A:
A(r) = $100(1 + r)t
a) Find the amount to which $100 will grow in 2 years at 6%.
b) The amount to which $100 will grow in 4 years at 17%.
When the question asks you to "[f]ind the amount to which $100 will grow in 2 years at 6%," the question is directly telling you the values of the unknowns, r and t.
The only part left to do is to substitute these values into the equation and solve.
\(A(r,t)=100(1+r)^t\\ A(0.06,2)=100(1+0.06)^2\\ A(0.06,2)=\$112.36\)
See if you can do the next one.
Hey, TheXSquaredFactor! I did the work with the frist one and I got the right answer so now I understand. Then I did the same method with the next one and this what I got:
A(r,t) = 100(1+r)^t
A(0.17,4) = 100(1+0.17)^4
A(0.17,4) = $187.388721
I suppose that this is right, but I don't know if I have to round the answer.
Good job, Rick! You should absolutely round to the nearest hundredth place. The context of this problem deals with money, and the smallest modern currency only comes in denominations of cents. Fitting this context requires you to round.