$[15]$ A company estimates that computers lose $9\%$ of their value each year. Assume that shipment of new computers, each costing $$1600,$ arrives today. Let $x$ equal the number of years from now.

$($a$)$ Find an exponential model to represent the value of a computer based on the number of years from now.

$($b$)$ How much will each computer be worth in five years?

$($c$)$ In how many years will each computer be worth less than $$875?$

$($d$)$ A computer is considered worthless when its value is less than $25\%$ of its original price. When will these computers become worthless?