Mathematics: Tristan purchased a new car in 2000 for $22,800. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $10,400 in the year 2006, then what would be the predicted value of the car in the year 2016, to the nearest dollar?

calories per gram:Fat: 9Carbohydrate: 4Protein: 4...

Tristan purchased a new car in 2000 for $22,800.

gabbym39077

27.01.2022

Cost of the car in year 2016 will be $2811.

Step-by-step explanation:

Cost price of the car = $22800

Value of the car has been depreciating exponentially, so the formula for value of the car after t years,

$P(t)=A(1-\frac{r}{100})^{t}$

Here P(t) = Final value after t years

A = Cost price or initial value

r = rate of depreciation

t = duration in years

$P(6)=22800(1-\frac{r}{100})^{6}$

$10400=22800(1-\frac{r}{100})^{6}$

$\frac{10400}{22800}=(1-\frac{r}{100})^{6}$

0.87737 = $(1-\frac{r}{100})$

r = 100(1 - 0.87737)

r = 12.26%

Now cost of the car in year 2016 (After 16 years)

P(16) = $22800(1-\frac{12.26}{100})^{16}$

= $22800(0.87737)^{16}$

= 2810.99

= $2811

Therefore, cost of the car in year 2016 will be $2811.

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