Answer
The doubling time of the function; $f\left( t \right)=2\cdot f\left( 0 \right)$, for the amount of time $t$, is true.
Work Step by Step
$f\left( t \right)=2\cdot f\left( 0 \right)$
$t$ is the amount of time for the function:
In the expression, the value of $f\left( t \right)$ is two times $f\left( 0 \right)$,
Thus,
$f\left( t \right)=2\cdot f\left( 0 \right)$
This is the doubling time of the function. Thus, the statement is $\fbox{true}$.