The value of a new car decreases exponentially.Suppose your mother buys a new car for 22,000. The value of the car decreases by 20% each year.
a.what is the initial price of the car. The decay factor.
b. write an equation to model the value of the cars years after she buys it.
c. Find the value of the car after 6 years.
a. The initial price of the car is $22,000.
The decay factor is 20%, which can be written as 0.20 in decimal form.
b. To model the value of the car years after she buys it, we can use the formula for exponential decay:
V(t) = V₀ * (1 - r)^t
Where:
V(t) is the value of the car after t years,
V₀ is the initial value of the car,
r is the decay factor,
t is the number of years.
Plugging in the values, the equation becomes:
V(t) = 22,000 * (1 - 0.20)^t
c. To find the value of the car after 6 years, we can substitute t = 6 into the equation:
V(6) = 22,000 * (1 - 0.20)^6
Calculating this:
V(6) ≈ 22,000 * (0.80)^6
V(6) ≈ 22,000 * 0.262144
V(6) ≈ $5,765.17
Therefore, the value of the car after 6 years is approximately $5,765.17.
a. The initial price of the car is given as $22,000.
b. To model the value of the car in subsequent years, we can use the equation for exponential decay:
V = P(1 - r)^t
Where:
V = Value of the car after t years
P = Initial price of the car
r = Decay factor (expressed as a decimal)
t = Number of years
In this case, the decay factor is 20%, which can be written as 0.20 when expressed as a decimal.
Therefore, the equation for the value of the car after t years would be:
V = 22,000(1 - 0.20)^t
c. To find the value of the car after 6 years, we can substitute t = 6 into the equation:
V = 22,000(1 - 0.20)^6
Simplifying the calculation:
V = 22,000(0.80)^6
Using a calculator:
V ≈ 9,830.84
Therefore, the value of the car after 6 years would be approximately $9,830.84.
value=22000*(.8)^t
c. value=22000*(.8)^6