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Jack bought a new car in 2014 for \$28,000.

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Jack bought a new car in 2014 for \$28,000. If the value of the car decreases by 14% each year, write an exponential model for the value of the car. Then, estimate the year the car will have a value of \$5,000.

Jan 30, 2019

#2
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\$5,000 = \$28,000 x 0.86^t           divide both sides by 28,000

0.178571 = 0.86^t                        take the log of both sides

t = log(0.178571) / log(0.86)

t = 11.42 =~11 1/2 - years when the car will be worth about \$5,000.

Jan 30, 2019

#1
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My model= 28000(0.86)^t

I don't get how to get the time though

Jan 30, 2019
#2
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\$5,000 = \$28,000 x 0.86^t           divide both sides by 28,000

0.178571 = 0.86^t                        take the log of both sides

t = log(0.178571) / log(0.86)

t = 11.42 =~11 1/2 - years when the car will be worth about \$5,000.

Guest Jan 30, 2019
#3
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Use desmos and put the formula

Y=28000*0.86^t

then put in y=5000 in another slide and see where they meet. thats the answer

Jan 30, 2019