A quantity $P$ is an exponential function of time $t,$ such that $P_0{a}^3=90$ and $P_0{a}^2=60.$ Use the given information about $P=P_0{a}^t$ to:

$($a$)$ Find values for the parameters a and $P_0.$

Round your answer for $P_0$ to three decimal places. Enter the exact answer for $a.$

$a=$

$P_0=$

$($b$)$ Give the initial quantity and the percent rate of growth or decay.

Round your answer for the initial quantity to three decimal places. Enter the exact answer for the percent rate of growth or decay.

The initial quantity is $$ and the quantity is $$ growing at a rate of $\%$ per unit time.