Jonas purchased a new car for $25,000. Each year the value of the car depreciates by 20% of its value the previous year. In how many years will the car be worth $5000?

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1 year

To find out in how many years the car will be worth $5000, we need to calculate the depreciation of the car's value each year until it reaches $5000.

Let's break down the problem step by step:

The car initially costs $25,000.

Each year, the car's value depreciates by 20% of its value the previous year. This means that the value after the first year is 80% of the initial value, after the second year it's 80% of the value after the first year, and so on.

We can set up an equation to represent this:

Value_after_n_years = Initial_value * (1 - Depreciation_rate)^n

Where:
- Value_after_n_years is the car's value after n years,
- Initial_value is the initial value of the car ($25,000 in this case),
- Depreciation_rate is the depreciation rate per year (20% or 0.2),
- n is the number of years.

We want to find the value of n when Value_after_n_years = $5000.

Let's substitute the given values into the equation:

$5000 = $25,000 * (1 - 0.2)^n

Now, we can solve for n.

Dividing both sides of the equation by $25,000, we get:

0.2^n = $5000 / $25,000

0.2^n = 0.2

To solve for n, we can take the logarithm of both sides of the equation:

log(0.2^n) = log(0.2)

n * log(0.2) = log(0.2)

Now, dividing both sides of the equation by log(0.2), we get:

n = log(0.2) / log(0.2)

Using a calculator, we can find the value of n to be approximately 5.0.

Therefore, the car will be worth $5000 in approximately 5 years.