Question

PLEASE HELPPP

A car was valued at $45,000 in the year 1991. The value depreciated to $12,000 by the year 2000.

A) What was the annual rate of change between 1991 and 2000?
r=-------------Round the rate of decrease to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
r=------------%

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2003 ?
value = $----------------Round to the nearest 50 dollars.

Answer 1

Step-by-step explanation:

A) To find the annual rate of change between 1991 and 2000, we can use the formula:

r = (Vf/Vi)^(1/n) - 1

where r is the annual rate of change, Vf is the final value, Vi is the initial value, and n is the number of years.

Plugging in the values given, we get:

r = (12000/45000)^(1/9) - 1

r = -0.0901

So the annual rate of change is -0.0901.

B) To express the rate of change as a percentage, we can multiply it by 100:

r = -0.0901 * 100

r = -9.01%

So the correct answer to part A in percentage form is -9.01%.

C) Assuming that the car value continues to drop by the same percentage, we can use the formula:

V = Vi * (1 + r)^n

where V is the final value, Vi is the initial value, r is the annual rate of change, and n is the number of years.

Plugging in the values given, we get:

V = 12000 * (1 - 0.0901)^3

V = 12000 * 0.729

V = 8748

Therefore, the value of the car in the year 2003 will be $8,750.