Question

A car was valued at $44,000 in the year 1993. The value depreciates to $15,000 by year 2002.

Answer 1

Answer:

The car will have lost it's total value by 2007.

Step-by-step explanation:

If initially the car was valued at 44,000$, and after 9 years it's value dropped to 15,000$, we can say that the car's value dropped in 29,000$. If we suppose that the drop is the same every year, we can say that it was of 3,222,2$ by each year.

This amount of money is the 7,3% of the initial value of the car (I multiplied 3,222,2 x 100 : 44,000).

a) The annual rate of change was of 7,3%.

b) There are 14 years between 1993 and 2007. If we multiply 7,3% by 14, we get that the car lost 102,2% of it's initial value.

Answer 2

Answer:

A) -$29000/9 years

B) The car has lost its value by year 2007

Step-by-step explanation:

The annual rate of change is given by: $\\=\frac{15000-44000}{2002-1993} \\=\frac{-29,000}{9} \\=- 3222.22$

Therefore, the equation of the line that describes this change of value in terms of years passed, is a line with the slope given by this rate of change, and that passes through the value $44000 at year zero. That is:

$y(x)=-3222.22x+44000$

In the year 2007,  2007-1993= 14 years have gone by, so the car's value can be obtained by replacing x with "14" in the formula for the line:

$y(14)=-3222.22(14)+44000\\y=-1111.11$

which being a negative number, means that the car has lost its value.