If you deposit $1000 in a savings account with an interest rate of r compounded annually, then the balance in the account after 3 years is given by the function b(c) = 1000(1 + r)3, where r is written as a decimal.
what interest rate will yield a balance of $1100 after 3 years?
a.
3.23%
c.
3.63%
b.
3.33%
d.
3.66%

With the given function and values, the interest rate "r" can be solved for by substituting the given values to the equation, and algebraically solving for the unknown value.

Given function B(c) = 1000(1 + r)^3
Where B(c) = 1100 

1100 = 1000(1+ r)^3

To isolate "r", get the cube root of both sides of the equation:
3√(1100) = 3√(1000) * 3√(1+r)^3
10.3228 = 10(1+r)

Divide both sides by 10
(10.3228)/10 = [10(1+r)]/10
1.03228 = 1 + r

Subtract 1 from both sides of the equation to isolate "r":
1.03228 - 1 = 1 + r - 1
r = 0.03228 = 3.23%

Therefore the interest rate that will yield a balance of $1100 after 3 years is 3.23%.