Gina buys a car for $13,500. The value is expected to depreciate by 15% per year.
Write an exponential function to model the value of the car. When will the value
fall below $3000?

Answer:

the value will fall below $3000 in the 7 th year because :

Step-by-step explanation:

15% of 13500 is 2025

On subtracting 2025 from 13500 every time we can see that the value keeps dropping.

So, we will get $3375 in year 6 and in year 7 we will get $1350 by subtracting 2025 from 3375.

Hence we will get 1350 at the 7th year.

After 6.79 years, the car's value will drop below $3,000.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Now, The following is a representation of the exponential function to model the car's value:

V(t) = 13500 (1 - 0.15)ⁿ

V(t) = 13500(0.85)ⁿ

Here, V(t) denotes the car's worth at time n in years, and 0.85 denotes the annual depreciation rate of 15%.

Hence, The following equation can be put up to determine when the car's value will drop below $3,000:

13500(0.85)ⁿ = 3000

As we solve for n, we obtain:

n = (log(3000/13500)/log(0.85))

n = 6.79

So, after roughly 6.79 years, the car's value will drop below $3,000.

Learn more about the percent visit:

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