A car depreciates by 8% of its initial value each year. If the car was worth $34,000 two years ago, how much is it worth now?

Answer 1

#=28777.6$#

In #2# years depreciation in the value of the car can be written as #34000(1-0.08)^2# #=34000(0.92)^2# #=34000(0.8464)# #=28777.6$#

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Answer 2

Jace Anderson

To find the current value of the car, we can use the formula for exponential decay, which is:

[ V = V_0 \times (1 - r)^t ]

Where:

( V ) is the current value of the car
( V_0 ) is the initial value of the car
( r ) is the rate of depreciation (expressed as a decimal)
( t ) is the time in years

Given that the car depreciates by 8% each year (or 0.08 as a decimal), and it was worth $34,000 two years ago, we can plug these values into the formula:

[ V = 34000 \times (1 - 0.08)^2 ]

[ V = 34000 \times (0.92)^2 ]

[ V = 34000 \times 0.8464 ]

[ V \approx 28789.6 ]

Therefore, the current value of the car is approximately $28,790.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.