The weekly cost $C$, in dollars, of manufacturing $x$ lightbulbs is $$C ( x ) =7500+ \sqrt{125x}$$

Solution (a) The weekly cost of manufacturing $100$ lightbulbs is $$C ( 100 ) =7500+ \sqrt{125\cdot 100}=7500+ \sqrt{12{,}500}\approx \$7611.80$$

The weekly cost of manufacturing $101$ lightbulbs is $$C ( 101 ) =7500+ \sqrt{125\cdot 101}=7500+ \sqrt{12{,}625}\approx \$7612.36$$

The average rate of change of the weekly cost $C$ from $100$ to $101$ is $$\dfrac{\Delta C}{\Delta x}=\dfrac{C ( 101 ) -C ( 100 ) }{ 101-100}\approx \dfrac{7612.36-7611.80}{1}=\$0.56$$

(b) The weekly cost of manufacturing $1000$ lightbulbs is $$C ( 1000) =7500+ \sqrt{125\cdot 1000}=7500+ \sqrt{125{,}000}\approx \$7853.55$$

The weekly cost of manufacturing $1001$ lightbulbs is $$C ( 1001) =7500+ \sqrt{125\cdot 1001}=7500+ \sqrt{125{,}125}\approx \$7853.73$$

The average rate of change of the weekly cost $C$ from $1000$ to $1001$ is $$\dfrac{\Delta C}{\Delta x}=\dfrac{C ( 1001) -C ( 1000) }{ 1001-1000}\approx \dfrac{7853.73-7853.55}{1}=\$0.18$$

(c) Part (a) tells us that the cost of manufacturing the 101st lightbulb is $0.56. From (b) we learn that the cost of manufacturing the 1001st lightbulb is only $0.18. The unit cost per lightbulb decreases as the number of lightbulbs manufactured per week increases.