Question

In 2003, Troy bought a new car for $33,500 . The car was worth $21,000 in the year 2011. If Troy knows that the value of the car depreciated linearly, what was the annual rate of change of the car's value? Round your answer to the nearest hundredth if necessary.

can someone help me?

Answer 1

In 2003, Troy bought a new car for $33,500 . The car was worth $21,000 in the year 2011. If Troy knows that the value of the car depreciated linearly,

Let x be the number of years and y be the cost of the car

Lets assume x=0 for 2003

for 2003, x=0 . so for year 2011 , x= 2011- 2003 = 8

When x=0, y = 33,500

When x= 8, y= 21,000

So two points are (0, 33500) and (8,21000)

To find annual rate of change we find slope because the car depreciated linearly.

`slope = (y_2-y_1)/(x_2- x_1)`

`slope = (21000-33500)/(8- 0)`

`slope = -(3125)/(2)`

Slope = -1562.50

The rate of change of car's value = -1,562.50