Every four years the value of a Chevy Cabalier is reduced by half.
Purchase price $15,375
After t years of ownership:
Age of car: Value:
0 15,375
4 7,687.50
8 3,843.75
If P is price after t years, Which would be a good model for the values above?
a) P(t) = 15,375 (2)^t
b) P(t) = 15,375 (1/2)^t
c) P(t) = 15,375 (1/2)^t/4
d) P(t) = 15,375 (2)^t/4
The general formula for a "half-life" problem is
Value = original(1/2) ^(t/k) , where k is the half-life period.
so what do you think?
I think C
To determine which model represents the given values, let's analyze the problem step by step.
We can see from the information provided that after every four years, the value of the Chevy Cavalier is reduced by half. This means that the value is halved every four years.
Let's examine the given table:
- When the age of the car is 0 years, the value is $15,375. This is the starting value.
- When the age of the car is 4 years, the value is $7,687.50. This value is half of the previous value.
- When the age of the car is 8 years, the value is $3,843.75. Again, this value is half of the previous value.
Now, let's look at the answer choices:
a) P(t) = 15,375(2)^t
b) P(t) = 15,375(1/2)^t
c) P(t) = 15,375(1/2)^(t/4)
d) P(t) = 15,375(2)^(t/4)
From the analysis of the problem, we can see that the value is always reduced by half every four years. Therefore, the correct answer would be option **b) P(t) = 15,375(1/2)^t**.
This equation represents the halving of the value every time the age of the car increases by four years.