Question

The value of a boat, in dollars, x years from its model year can be predicted by the function f(x)=14,000(0.88)x .

The value of a certain yacht, in dollars, x years from its model year can be predicted by the exponential function shown in the table.

How much more will the boat be worth than the yacht 5 years after their model years?


Enter your answer, rounded to the nearest cent,


x ​g(x)​

0 18,000

1 14,580

2 11,809.80

3 9565.94


4 7748.41

5 6276.21

Answer 1

the boat will be worth 1,112.04 more than the yacht in 5 years

Explanation:

The value of a boat, in dollars, x years from its model year can be predicted by the function

`f(x)=14000(0.88)^x`

Now we find the value of boat in 5 years, we plug in 5 for x

`f(5)=14000(0.88)^5`

`f(5)=14000(0.527731916)`

f(5)= 7388.25

so the value of the boat in 5 years = $7,388.25

From the given table, x=5 then g(x) = 6,276.21

The value of yacht in 5 years = $6,276.21

Now we find the difference between the values

7388.25 - 6276.21= 1112.04

the boat will be worth 1,112.04 more than the yacht in 5 years

Answer 2

1112.04 Using the function f(x) = 14000*0.88^x for x = 5, we get f(x) = 14000*0.88^x f(5) = 14000*0.88^5 f(5) = 14000*0.527731917 f(5) = 7388.246835 f(5) = 7388.25 Which indicates that the boat will be worth $7388.25 after 5 years. Using the lookup table for the yacht, the yacht will be worth $6276.21 after the same 5 years. Subtracting this value from the value of the boat: $7388.25 - $6276.21 = $1112.04 Tells us that the boat is worth $1112.04 more than the yacht after 5 years.