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If a boat costs $40,000 find the number of years until the boat is worth $18,000....

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swavers | Student, Grade 11 | eNoter

Posted February 10, 2011 at 7:45 AM via web

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If a boat costs $40,000 find the number of years until the boat is worth $18,000.  [Round the answer to the nearest tenth of a year.]

A new boat will decrease in value at a rate of 8% per year according to this formula V=C(1-r)^t  where V is the value of the boat after t years, C is the original cost, and r is the rate of depreciation. If a boat costs $40,000 find the number of years until the boat is worth $18,000.  [Round the answer to the nearest tenth of a year.]

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted February 10, 2011 at 8:16 AM (Answer #1)

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Given the formula:

V = C(1-r)^t

v is the values

c is the original cost = 40,000

r is the rate = 8% = 0.08

t is the number of years

Given the information above, we need to find t such that v= 18,000

We will substitute the given information into the equation.

==> 18,000 = 40,000 *( 1- 0.08)^t

==> 18,000 = 40,000*(0.92)^2

We will divide by 40,000

==> (0,92)^t = 0.45

Now we will take the logarithm for both sides.

==> log (0.92)^t = log 0.45

==> t* log (0.92) = log 0.45

==> t= log 0.45 / log 0.92 = 9.6 years

Then, it takes 9.6 years for the boat to be worth $18,000.

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