MATH SOLVE

5 months ago

Q:
# 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 βg(x)β0 18,0001 14,5802 11,809.803 9565.944 7748.415 6276.21

Accepted Solution

A:

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.