Exponential Equations 22

Question

A computer purchased for $800 loses 10% of its value every year.The computer's value can be modeled by the function , where  is the dollar value and  the number of years since purchase.

(A) In the exponential model  ___ and  .

(B) In how many years will the computer be worth half its original value? ___Round answer to 1 decimal place.The answer is__  years

Answer 1

1/2 = e^-.10t

t = (ln.5)/-.1 = -10ln.5 = about 6.93 years = half life = about 6.9 years

or

800(.9)^t with a=800 b= .9

400 = 800.9^t

1/2 = .9^t

t = log.5 to the base .9 = ln.5/ln.9 = about 6.6 years

6.9 is with continuous depreciation

6.6 is with just annual depreciation