Question

A boat costs $11,850 and decreases in value by 10% per year. How much will the boat be worth after 8 years?

A. $4,590.93

B. $11,770.00

C. $25,401.53

D. $5,101.04

Answer 1

11,850 x .9 = 11,605

11605 x . 9 = 9,598.5 year 2

9,598.5 x .9 = 8,638.65

8,635 x .9 = 7,774.785 year 4

7,774.785 x .9 = 6,997.31

6,6997.31 x .9 = 6297.58 year 6

6297.58 x .9 = 5,667.82

5,667.82 x .9 = 5,101.04 year 8

The answer is D

Answer 2

The boat worth is $5101.04 after 8 years .

Option D is correct .

Explanation:

The decrease exponential function is written in the form

`y = a (1 - r)^(t)`

Where a is the initial value , r is the rate of interest in the decimal form and t is the time in years .

As given

A boat costs $11,850 and decreases in value by 10% per year .

a = $ 11850

10% is written in the decimal form

`= (10)/(100)`

= 0.10

t = 8 years

Put all the values in the function

`y = 11850(1 - 0.10)^(8)`

`y = 11850(0.9)^(8)`

`y = 11850* 0.430467`

y = $5101.04

Therefore the boat worth is $5101.04 after 8 years .

Option D is correct .