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

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.

Answer 2

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.