Answer
$69.078=t$
Becoming a millionaire would take 69 years.
Work Step by Step
The future value of a continuous compound rate can be described with the following function:
$A(t)=P*e^{rt}$, where $P$ is the amount of investment at $t=0$, $r$ is the compound rate and $t$ is the time since the investment.
In this exercise:
$A(t)=1,000,000$
$P=1,000$
$r=0.1$
Therefore the question is to calculate $t$, such as:
$1,000,000=1,000*e^{0.1t}$
$\frac{1,000,000}{1,000}=e^{0.1t}$
$\log_{e}1,000=\ln1,000=6.9078=0.1t$
$69.078=t$
Becoming a millionaire would take 69 years.