A population, $P(t)$ (in millions) in year $t$, increases exponentially. Suppose $\ P(7)=21 \ $ and $\ P(13)= 30$.
 
a) Find a formula for the population in the form $P(t)= ab^t$. Enter the values you found for a and b in your formula in the blanks below. Round your values to 4 decimal places.
$\ \ \ \ a =$ $\ \ \ \ b =$
 
b) If $P(t)=ae^{kt}$, what is the value of $k$ in your formula.
$\ \ \ \ k =$ (round to 4 decimal places)