The demand for ceiling fans can be modeled below as

D$($p$)=25\mathrm{.}02(0\mathrm{.}996^$p$)$ thousand ceiling fans

where p is the price $($in dollars$)$ of a ceiling fan.

$($a$)$ According to the model, is there a price above which consumers will no longer purchase fans? Explain why or why not.

The model is exponential and crosses does not cross the horizontal axis. Therefore there is a price is no price above which consumers will not purchase a ceiling fan.

$($b$)$ Calculate the amount that consumers are willing and able to spend to purchase $15$ thousand ceiling fans. $($Round your answer to three decimal places.$)$

$$5657\mathrm{.}250$ thousand

$($c$)$ How many fans will consumers purchase when the market price is $$100?($Round your answer to three decimal places.$)$

$$16\mathrm{.}758$ thousand fans

$($d$)$ Find the consumers' surplus when the market price is $$100.($Round your answer to three decimal places.$)$

$$\_\_\_\_\_\_\_$ thousand