I first want to make it clear that I have only taken Geometry, Algebra I, and pre-Algebra. That seemed to clear things up last time.
Question:
Matt bought a car at the cost of 25,000 dollars. This car's value goes down 15% every year.
1. What is the decay factor?
2. Write the equation to model the decay factor.
3. What will the car be worth in 5 years?
If something decreases by 15%, then 85% would be left over.
equation:
value = 25000(.85)^t , where t is the number of years
so in 5 years, t - 5
value = 25000(.85)^5 = ......
Thank you c:
To answer these questions, we need to understand the concept of decay factors and how they can be applied in this scenario. Decay factors are used to represent the decrease or decay of a quantity over time.
1. The decay factor is the percentage decrease per unit of time. In this case, the car's value goes down by 15% every year. To convert this percentage to a decimal, we divide it by 100. So, the decay factor is 0.15 (15/100).
2. To model the decay factor, we can use the equation:
Value after n years = Initial value × (1 - decay factor)^n
In this case, the initial value (V0) is $25,000 and the decay factor is 0.15. The equation becomes:
Value after n years = $25,000 × (1 - 0.15)^n
3. To find out what the car will be worth in 5 years, we substitute n = 5 into the equation:
Value after 5 years = $25,000 × (1 - 0.15)^5
Now, let's calculate the answer
Value after 5 years = $25,000 × (0.85)^5
Value after 5 years ≈ $13,970.43
Therefore, the car will be worth approximately $13,970.43 in 5 years.