The value of a $20,000 car decreases every, t. The equation below model this situation.
20,000(1-0.04t) = 13,000
How many years will the car be worth $13,000? Round to the nearest tenth if necessary.
I got 20,000(.96t)= 13,000, but I don't believe gives me the correct answer. Help!
this does not make sense:
" decreases every, t "
did it say it decreased 4% per year?
that would mean
.96^n =13/20
.96^n = .65
n log .96 = log .65
n = -.187/-.0177
= 10.6 years
I understand most of the explanation except the part below:
n log .96 = log .65
n = -.187/-.0177
Could you please explain? Thanks
To find the number of years the car will be worth $13,000, we need to solve the equation:
20,000(1 - 0.04t) = 13,000.
Let's solve this step by step:
1. Distribute the 20,000 to each term on the right side of the equation:
20,000 - 800t = 13,000.
2. Move the constant term to the right side of the equation:
-800t = 13,000 - 20,000.
-800t = -7,000.
3. Divide both sides of the equation by -800 to isolate 't' on one side:
t = -7,000 / -800.
t ≈ 8.75.
So, according to the calculations, it would take approximately 8.75 years for the car to be worth $13,000.
However, since time cannot be negative, we need to consider the positive value of 't'. Therefore, rounding to the nearest tenth, the car will be worth $13,000 after approximately 8.8 years.