Answer
a. 32968.4;
b. $73372.4.
Work Step by Step
a. $P=\int ^{10}_{0} 5000e^{-0.01t}.e^{-0.08t}=5000\frac{e^{-0.09t}}{-0.09}|^{10}_{0}=\frac{-5000}{0.09}(e^{-0.9}-1) \approx 32968.4 $
b. $A=e^{(0.08)10}\int^{10}_{0}5000e^{-0.01t}.e^{-0.08t}dt = e^{0.8}.5000\int^{10}_{0}e^{-0.09t}dt=e^{0.8}.5000.\frac{1}{-0.09}(e^{-0.09t}|^{10}_{0}) \approx 73372.4$
