Question

Bryan purchases a new boat. The expression below represents the value of the boat after x years. 22000(.88)^(x+2) Which statement is true?

A.The price of the boat decreases by 88% every year.
B.The price of the boat increases by 88% every year.
C.The price of the boat decreases by 12% every year.
D.The price of the boat increases by 12% every year.

Answer 1

For this case we have an equation of the form:

`y = A * (b) ^ x`
Where,
A: initial price
b: rate of change
x: time
When 0 <b <1, then the function decreases.
For this case we have the following function:

`y = 22000 (.88) ^ (x + 2)`
Where,

`b = 0.88`
We observe that the function decreases.
The percentage of decrease is given by:

`(1-0.88) * 100 = 12`
Answer:
C.The price of the boat decreases by 12% every year.

Answer 2

The formula for the growth rate is given by

`y=a(b)^x`

Now when b is greater than 1 , then it is increasing function

and when b is less than 1 , then it is decreasing function.

Now in the function

`22000(.88)^((x+2))`

here value of b is 0.88 , which is less than 1 , so it is decreasing function

And decay rate is given by

1-r = 0.88

Subtract 1 from both sides

-r = 0.88-1

-r = -0.12

r = 0.12

or r= 12%

It means it is decreasing at a rate of 12%

Hence Option C is correct

C.The price of the boat decreases by 12% every year.