Question

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

Answer 1

(1.006)^12t

Explanation:

I just did it on UsaTestPrep.

(1.08^1/12)^12t ≈ (1.006)^12t

Hope this helps!

Answer 2

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 =
`(1)/(12) * 12 t`
and the properties of exponents to rewrite the
model in a form that reveals the monthly growth rate.


`1.08^(t) = 1.08^((1/12)(12t)) = (1.08^(1/12)) ^(12t) = 1.0064634^(12t)`