The function below gives the value of Evan's truck t years after he purchased it.
v(t) =. 8,000(0.92)exponant of t
Which of the following is the meaning of the number 0.92 in this function for this situation?
A.
It shows that the car's value decreases by 92% each year.
B.
It shows that the car's value increases by 8% each year.
C.
It shows that the car's value decreases by 8% each year.
D.
It shows that the car's value increases by 92% each year.
C. It shows that the car's value decreases by 8% each year.
The correct answer is:
C. It shows that the car's value decreases by 8% each year.
Explanation:
In the given function, v(t) = 8,000(0.92)^t, the number 0.92 represents the rate at which the car's value decreases each year. Since the value is less than 1, it indicates a decrease. Specifically, the value decreases by 8% each year because 0.92 is equal to (100% - 8%).
To determine the meaning of the number 0.92 in the given function, let's break down the function.
v(t) = 8,000(0.92)^t
Here, "t" represents the number of years after Evan purchased the truck. The exponent "t" denotes the multiplicative effect on the original value.
In this case, the original value is 8,000. The number 0.92 represents the fraction of the previous value that remains after each year.
To find the meaning, we can compare the original value to the value after one year:
v(1) = 8,000(0.92)^1 = 8,000(0.92) ≈ 7,360
As we can see, after one year, the truck's value decreases to approximately $7,360.
Now, let's analyze the answer choices based on our findings:
A. It shows that the car's value decreases by 92% each year.
This is incorrect because the value decreases to 92% of the previous year's value, not by 92% each year.
B. It shows that the car's value increases by 8% each year.
This is also incorrect since the value decreases each year, not increases.
C. It shows that the car's value decreases by 8% each year.
This is the correct answer! The value decreases by 8% each year, as evidenced by the calculation above.
D. It shows that the car's value increases by 92% each year.
This is incorrect since the value decreases each year, not increases.
Therefore, the correct answer is C. It shows that the car's value decreases by 8% each year.