Question 1124886

Jasmine's car was worth ${{{11000}}} at the beginning of {{{2000}}} and the value of the car decreased exponentially, decreasing by {{{20}}}% each year.



use depreciation formula:
{{{v = c(1-r)^t}}}
where:
{{{v}}} = future value
{{{c}}} = current value
{{{r}}} = depreciation {{{rate}}} per period
{{{t }}}= number of periods

a. Write a function {{{f}}} that determines the value of Jasmine's car (in dollars) in terms of the number of years {{{t}}} since the beginning of {{{2000}}}.

since the beginning of {{{2000}}} to this year, there is {{{18}}}

{{{v = c(1-r)^18}}}

if car was worth ${{{11000}}} at the beginning of {{{2000}}} , and the value decreasing by {{{20}}}%={{{0.20}}} each year
 this year is worth:

{{{v = 11000(1-0.20)^18}}}

{{{v = 11000(0.80)^18}}}

{{{v = 198.16}}}

b. How many years after the beginning of {{{2000}}} was Jasmine's car worth ${{{6000}}}?

{{{6000 = 11000(1-0.20)^t}}}

{{{6000 /11000=(0.80)^t}}}

{{{6 /11=(0.80)^t}}}

{{{log(6 /11)=log((0.80)^t)}}}

{{{log(0.5454545454545455)=t*log(0.80)}}}

{{{t=log(0.5454545454545455)/log(0.80)}}}

{{{t=2.7}}} ->little over {{{2}}} and half years; so, it was in {{{2003}}}


c. How many years after the beginning of {{{2000}}} was Jasmine's car worth ${{{3400}}}? 

{{{3400 = 11000(1-0.20)^t}}}

{{{3400 /11000=(0.80)^t}}}

{{{34 /110=(0.80)^t}}}

{{{log(17 /55)=log((0.80)^t)}}}

{{{log(0.3090909090909091)=t*log(0.80)}}}

{{{t=log(0.3090909090909091)/log(0.80)}}}

{{{t=5.3}}} ->little over {{{5}}} years and three months; so, it was in at beginning of  {{{2006}}}