Answer
a)
Estimate = $470.75$
Actual = $470.747$
b)
average cost per camera is $485.25$
Work Step by Step
a)
Estimate
$C'(x)$ = $500-0.006x+(3\times{10^{-8}})x^{2}$
$C'(5000)$ = $500-(0.006\times5000)+(3\times{10^{-8}})(5000)^{2}$ = $470.75$
Actual
$C(5000)$ = $(500\times5000)-(0.006\times5000^{2})+(3\times{10^{-8}}\times5000^{3})$ = $2426350$
$C(5001)$ = $(500\times5001)-(0.006\times5001^{2})+(3\times{10^{-8}}\times5001^{3})$ = $2426720.747$
$C(5001)-C(5000)$ = $2426720.747-2426350$ = $470.747$
b)
$\frac{C(x)}{x}$ = $\frac{2426350}{5000}$ = $485.25$
average cost per camera is $485.25$
