1.08t can be written as (1.081/12)12t to give the approximate equivalent monthly interest rate based on an annual rate of 8%. Use the properties of exponents to transform the expression into a single exponent expression

Because t is given in years and 1.08 = 1 + 0.08, the annual percent increase
is 8%.
To find the monthly percent increase that gives an 8% annual increase,
use the fact that
t = [tex] \frac{1}{12} * 12 t[/tex]
and the properties of exponents to rewrite the
model in a form that reveals the monthly growth rate.

[tex] 1.08^{t} = 1.08^{(1/12)(12t)} = (1.08^{1/12}) ^{12t} = 1.0064634^{12t} [/tex]