in 2016, you purchased a new car for $20,000. The value of the car depreciates at a rate of 18% per year. The value V of the car after t years is given by the function V(t)=20000(0.82)t. When will the car be worth three-quarters of its original value?
V = Vi (0.82)^t not times t
.75 = .82^t
log .75 = t log .82
t = log.75 / log.82 = 1.45 years
To find out when the car will be worth three-quarters of its original value, we need to solve the equation:
V(t) = 0.75 * $20,000
where V(t) represents the value of the car after t years.
Substituting the equation for V(t) with the given formula, we have:
20000(0.82)^t = 0.75 * 20000
Now, divide both sides of the equation by 20000:
(0.82)^t = 0.75
To solve for t, we need to take the logarithm (base 0.82) of both sides:
log(0.82)^t = log(0.75)
Using the logarithm power rule, we can bring down the exponent:
t * log(0.82) = log(0.75)
Now, divide both sides of the equation by log(0.82):
t = log(0.75) / log(0.82)
Using a calculator, we can evaluate this expression to find the value of t.