A car was purchased for $3,495 and will depreciate 20% of the original price each year.
Find a linear function for the value of the car at time t in years. Define variables clearly.
Graph the function you found in part A.
A claim is made that the car will not be worth anything in five years. Do you agree with this claim?
Explain. In your explanation include the following:
State the problem in your own words.
Describe the strategy used to solve the problem.
Clearly state your answer and explain why it is reasonable.
Tell whether you agree with the claim, explaining why or why no
v = 3495 - (3495/5)t
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To find a linear function for the value of the car at time t in years, let's define the variables:
V(t) = value of the car at time t
P = original purchase price of the car
r = annual depreciation rate (as a decimal)
Based on the given information, we know:
P = $3,495
r = 20% = 0.20
To find V(t), we can use the formula for linear depreciation:
V(t) = P - r * P * t
Plugging in the given values, we get:
V(t) = 3,495 - 0.20 * 3,495 * t
Now, let's graph this function to visualize the value of the car over time.
Assuming we have a suitable graphing tool, we can plot the points by substituting different values for t into the function. For example, at t = 0, the car is just purchased and the value is $3,495. As t increases, we can determine the corresponding values V(t) to plot on the graph.
Now, let's address the claim that the car will not be worth anything in five years.
The problem is asking whether the value of the car will be zero after five years, considering the given depreciation rate of 20% per year.
To solve this problem, we can substitute t = 5 into the function V(t) = 3,495 - 0.20 * 3,495 * t. This will give us the value of the car after five years.
V(5) = 3,495 - 0.20 * 3,495 * 5
= 3,495 - 0.20 * 17,475
= 3,495 - 3,495
= 0
From the calculation, we can see that the value of the car is indeed zero after five years, confirming the claim made.
I agree with the claim that the car will not be worth anything in five years based on the given information and calculations. The linear function representing the value of the car indicates a steady decline over time due to the 20% annual depreciation. Therefore, it is reasonable to conclude that after five years of depreciation, the value will depreciate to zero.