Harper buys a car in 2007 for $20000. Each year,the car decreases in value by 18%. How much will the car be worth in 2012? round to the nearest cent
Is the common ratio 0.18? If not please help me
No
Think of how you would obtain the next term
you could take .18 of the previous term and subtract or just take .82 of it
so the sequence is:
20000 , 20000(.82), 20000(.82)^2 , ....
so r = .82
I am sure you can now answer the question
To find the value of the car in 2012, we need to calculate the decrease in value each year. The decrease in value is given as 18% or 0.18.
To calculate the value of the car each year, we can use the formula for compound interest:
Value in a year = Initial Value * (1 - Decrease Rate)^Number of Years
In this case, the initial value is $20,000, the decrease rate is 0.18, and the number of years is 2012 - 2007 = 5.
Using the formula, we can calculate the value of the car in 2012:
Value in 2012 = $20,000 * (1 - 0.18)^5
Now let's compute it.
Value in 2012 = $20,000 * (0.82)^5
Value in 2012 ≈ $20,000 * 0.380204
Value in 2012 ≈ $7,604.08
Therefore, the car will be worth approximately $7,604.08 in 2012 (rounded to the nearest cent).