The equation $A(t)=8000e^{0\mathrm{.}05t}$ gives the balance after $t$ years of an initial investment of $8000$ dollars which pays $5\mathrm{.}00\%$ compounded continuously.

a$.$ Find a formula for $\frac{dA}{dt}$

b$.$ Find and interpret $A^{\text{'}}(8).$ Include appropriate units.

c$.$ Compare the approximation of $$597$ to the actual change. Report your answer to two decimal places.

a$.\frac{dA}{dt}=$