If you invest $100 into an account that earns 9% interest each year, how many years will it take for you to have $200?

It does not say simple or compound interest.

Simple interest is rarely used these days, so assume compound.

Use the standard formula:

future value = present value * (1+rate/n) ^ (nt)

n=number of times interest is compounded per year (=1)

t=number of years

Plugging values,

200=100 (1.09) ^t

1.09^t = 2

take log

t (log (1.09)) = log 2

t=log (2) / log (1.09) = 0.6931/0.08618=8.04 years.