The demand function for a product is

$D(x)=64-x^2$

and the supply function is

$S(x)=3x^2$

a$.$ Find the equilibrium point.

b$.$ Find the consumer's surplus. Include a shaded graph with your answer.

c$.$ Find the producer's surplus. Include a shaded graph with your answer.

Continuous Money Flow. Find the total income in $8$ years by a continuous

money flow with a rate of $f(t)=e^{0\mathrm{.}06t}$ and the present value in $8$ years with

$r=10\%.$

Hint: You may need to look at the formulas in Section $13\mathrm{.}4.$