Question

After a new $28,000 car is driven off the lot, it begins to depreciate at a rate of 18.9% annually.
Which function describes the value of the car after t years?

1)C(t) = 28,000(0.158)^t
2)C(t) = 28,000(0.811)^t
3)C(t) = 28.000(1.575)^t
4)C(t) = 28.000(0.189)^t​

Answer 1

Answer:

2

Step-by-step explanation:

We get 0.811 as our depreciating value because we take 18.9% and turn it into a decimal. Then, we subtract that from 1. If we did 0.189 instead, it would depreciate at a rate of 81.1% annually.

Answer 2

The function $C(t) = 28,000(0.811)^t$ describes the value of the car after t years.

What is the compound interest formula for finding depreciation?

The formula for finding the value of an amount using compound interest is given:

$A = P(1+i)^t$

Where A is the amount,

P is the principal,

i is the interest rate,

And t is the number of years.

Similarly, the formula using compound interest to find depreciation is given by:

$A = P(1-i)^t$

We can find the function as shown below:

The original price is given as $28,000.

The rate of depreciation is given as 18.9%.

The formula for finding depreciation using compound interest is given by:

$A = P(1-i)^t$

Now, substitute the value of P and i:

$A = 28,000(0.811)^t$

Now compare this with the options given.

Option 1 is not the correct answer as it does not have 0.811.

Option 2 is the correct answer as it matches the formula that we found.

Option 3 is not the correct answer as it does not have 0.811.

Option 4 is not the correct answer as it does not have 0.811.

Therefore, we have found that the function $C(t) = 28,000(0.811)^t$describes the value of the car after t years.

Learn more about compound interest here: https://brainly.com/question/24924853

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