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.]
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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