Functions Word Problem

by Pujan
(Ny, usa)

The value of a 1996 Mustang, in thousands of dollars, is a function of the age a of the car, in years. Let V=f(a) be the function that represents the value of the car when it is a years old. Assume V is a linear function. (a) Interpret the equation f(3)=27 in practical terms. (b) If Mustang was bought for $35,000 in 1996, find a formula for V. (c) Graph V

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Functions Word Problem

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Oct 14, 2010
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by: Karin

This is a great problem for the functions unit.

a. f(3) = 27 means that the car's value after 3 years was 27,000. Remember the original equation was v = f(a). 3 takes the place of a which was the age and 27 takes the place of V which is the value in thousands.

b. In order to write an equation, you must first write two points. We can write the points based on the age of the car (x) and the value of the car (y).

We know that in 1996, when the car was purchased, the value was 35,000. In terms of age, the car was 0 years old because it was just purchased.
So, (0, 35,000)

We also know from above that at 3 years old, the value of the car is 27,000. So, (3, 27000) is the other point.

Now we have (0, 35,000) & (3, 27,000)

First we must find the slope using the slope formula.

y(sub2) - y(sub1)/ x(sub2) - x (sub1)

(I can't write subscripts, so sub 1 and sub 2 just refers to either point 1 or point 2)

Step 1: 27000 - 35000 / 3 - 0

-8000/3

m = -2666.67

The slope is -2666.67 which means that each year, the car value decreases by $2666.67.

So, we know the slope is -2666.67 and we also know the y-intercept is 35000 because this is the beginning value, when x = 0.

Now we can write the equation:
f(a) = -2666.67a + 35000

c. In order to graph this equation, you can plot the two points (0, 35000) and (3, 27000). It is a linear equation, so it will produce a straight line.

I hope this helps,
Karin

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