A new car is purchased for $24,800 the value of the car a depressant case at 12% per year what will the value of the car be to the nearest cent after 13 years

$4706.80731

Step-by-step explanation:

Car purchase is $24800

Per year it depressant by 12%

100-12=88%

For year 1 is 0.88×24800= $21824

Year 2 is 0.88×$21824= $19205.12

Year 3 is 0.88×$19205.12 = $16900.5056

Year 4 is 0.88×$16900.5056 =$14872.445

Year 5 is 0.88 × $14872.445= $13087.7515

Year 6 is 0.88×$13087.75154= $11517.22136

Year 7 is 0.88× $11517.22136= $10135.1548

Year 8 is 0.88× $10135.1548= $8918.936

Year 9 is 0.88× $8918.936= $7848.664

Year 10 is 0.88× $7848.664= $6906.824

Year 11 is 0.88× $6906.824= $6078.005

Year 12 is 0.88×$6078.005= $5348.645

Year 13 is 0.88× $5348.645= $4706.8073

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: