The value, V, of a $25000 vehicle after y years is given by V = 25000 (0.85)^y
What is the rate of depreciation?
What will the car be worth after 5 years?
To the nearest month, how long would it take to reduce the vehicle’s value to 10% of its original amount?
The rate of depreciation would be 15%
(.85= 1 - .15)
after 5 years
V = 25000(.85)^5 = ...
last part:
when V = 2500
25000(.85)^y = 2500
.85^y = .1
take log of both sides
log .85^y = log .1
y log.85 = log.1
y = log.1/log.85 = 14.168 years
= 14 years and appr 2 months
To find the rate of depreciation, we can compare the original value V0 with the value after one year V1.
After 1 year, the value of the vehicle is given by V1 = 25000 * (0.85)^1.
The rate of depreciation is the difference between the original value and the value after one year, divided by the original value:
Rate of depreciation = (V0 - V1) / V0.
Substituting the values:
Rate of depreciation = (25000 - 25000 * (0.85)^1) / 25000.
Simplifying this expression gives us the rate of depreciation.
To find the value of the vehicle after 5 years, we can use the given formula:
V = 25000 * (0.85)^y.
Substituting y = 5 into the equation, we get:
V = 25000 * (0.85)^5.
Evaluating this expression will give us the value of the vehicle after 5 years.
To find the time it takes for the vehicle's value to reduce to 10% of its original amount, we need to solve the equation:
V = 25000 * (0.85)^y,
where V is the value we are looking for (10% of the original value), and we solve for y.
Setting V equal to 0.1 times the original value, we have:
0.1 * 25000 = 25000 * (0.85)^y.
Simplifying the expression and taking the logarithm of both sides will enable us to solve for y. After solving for y, we can round to the nearest month.