A computer purchased for 1650 loses 19 of its value every ye

A computer purchased for $1,650 loses 19% of its value every year.The computer\'s value can be modeled by the function v (t) = a*b^t, where v is the dollar value and t the number of years since purchase.

a. in the exponential modeel a=____ and b=_____

b. In how many years will the computer be worth half its original value? Round answer to 1 decimal place.

Solution

computer\'s value can be modeled by the function v (t) = a*b^t, where v is the dollar value and t the number of years since purchase.

at t=0 v(t) = $1650

at t=1 v(t) = $( 1650 -0.19*1650) = $1336.5

So, at t=0 v= a*b^0----> v = a

So, a = 1650

Now v(t) = 1650*b^t

At t=1 v = 1336.5.So, 1336.5 = 1650*b^1

b =0.81

a) So, a = 1650 ; b = 0.81

b) value become half in t years Find t

1650/2 = 1650 *0.81^t

0.5 = 0.81^t

Taking log on both sides: log0.5 = t*log0.81

t = 3.289 = 3.3 years