In a financial model, the amount $A$ grows according to $\frac{dA}{dt}=h\left(A\right)$. What role does the function $h\left(A\right)$ play in determining $A\left(t\right)$?

$h\left(A\right)$ determines the rate at which $A$ changes and thus shapes $A\left(t\right)$

$h\left(A\right)$ only sets the initial amount of $A$

$h\left(A\right)$ is not involved in the solution for $A\left(t\right)$

$h\left(A\right)$ only affects the time variable, not $A\left(t\right)$