64Percent growth per year

The value of an investment, in dollars, $\displaystyle t$ years after it was made is $\displaystyle f(t) = 500(1.21)^{t/2}$. By what percent does the value increase each year? A) 10% B) 10.5% C) 21% D) 42%

The value increases by 10% each year, answer A. Since f(t) = 500(1.21)^(t/2) = 500(1.21^(1/2))^t, the yearly growth factor is √1.21 = 1.1, which is a 10% increase. Check: 1.1² = 1.21, matching the original 2-year factor.