A new car is purchased for 17000 dollars. The value of the car depreciates at 12.25% per year. What will the value of the car be, to the nearest cent, after 14 years?

To solve this problem, we will use the formula for exponential decay, which is:

V = P * (1 - r)^t

where:

• V is the final value of the car
• P is the initial value of the car
• r is the rate of depreciation
• t is the time in years

Given in the problem: P = $17,000 r = 12.25% = 0.1225 (as a decimal) t = 14 years

Substituting these values into the formula, we get:

V = 17000 * (1 - 0.1225)^14

Now, calculate the value inside the parentheses:

1 - 0.1225 = 0.8775

Then raise this result to the power of 14:

0.8775^14 ≈ 0.0874

Finally, multiply this result by the initial value of the car:

V = 17000 * 0.0874 ≈ $1485.80

So, the value of the car after 14 years, to the nearest cent, will be approximately $1485.80.

To solve this problem, we will use the formula for exponential decay, which is:

V = P * (1 - r)^t

where:

• V is the final value of the car
• P is the initial value of the car
• r is the rate of depreciation
• t is the time in years

Given in the problem: P = $17,000 r = 12.25% = 0.1225 (as a decimal) t = 14 years

Substitute these values into the formula:

V = 17000 * (1 - 0.1225)^14

Now, calculate the value inside the parentheses:

1 - 0.1225 = 0.8775

Then raise this result to the power of 14:

0.8775^14 ≈ 0.0874

Finally, multiply this result by the initial value of the car:

V = 17000 * 0.0874 ≈ $1485.80

So, the value of the car after 14 years, to the nearest cent, will be approximately $1485.80.