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QuestionA car worth \22,500decreasesby$3200peryearfor6years.Define22,500 decreases by \$3200 per year for 6 years. Define V(x)for for 0 \leq x \leq 6andfind and find V(3)$.

Studdy Solution

STEP 1

Assumptions1. The initial purchase price of the car is 22,500..Thevalueofthecardecreasesby22,500. . The value of the car decreases by 3,200 per year for the first six years.
3. The value of the car, VV, after xx years is asked, where 0≤x≤60 \leq x \leq6.

STEP 2

First, we need to define the function that describes the value of the car after xx years. The value of the car decreases by ,200eachyear,sowesubtract,200 each year, so we subtract ,200x$ from the initial value of the car.
V(x)=Initial value−Decrease per year×xV(x) = Initial\, value - Decrease\, per\, year \times x

STEP 3

Now, plug in the given values for the initial value and decrease per year to define the function.
V(x)=$22,500−$3,200×xV(x) = \$22,500 - \$3,200 \times x

STEP 4

Now that we have the function, we can find the value of the car after3 years by substituting x=3x =3 into the function.
V(3)=$22,500−$3,200×3V(3) = \$22,500 - \$3,200 \times3

STEP 5

Perform the multiplication.
V(3)=$22,500−$9,600V(3) = \$22,500 - \$9,600

STEP 6

Subtract to find the value of the car after3 years.
V(3)=$22,500−$9,600=$12,900V(3) = \$22,500 - \$9,600 = \$12,900The value of the car after3 years is $12,900.

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