Answer:
D
Step-by-step explanation:
We know that the equation for the depreciation of the car is:
Where y is the current cost, A is the original cost, r is the rate of depreciation, and t is the time, in years.
We are told that the value of the car now is half of what it originally cost. So:
Substitute this for y:
We also know that the rate of depreciation is 10% or 0.1. Substitute 0.1 for r:
So, let's solve for t. Divide both sides by A:
Subtract within the parentheses:
Take the natural log of both sides:
Using the properties of logarithms, we can move the t to the front:
Divide both sides by ln(0.9):
Use a calculator. So, the car is approximately:
Our answer is D.
And we're done!