A vehicle depreciates according to the formula: v=29800(3.31)^-.06x where x is the age of the car in years. Find the value of the car when it is 15 years old.
Round to nearest whole number
To find the value of the car when it is 15 years old, we substitute x = 15 into the formula:
v = 29800(3.31)^(-0.06x)
v = 29800(3.31)^(-0.06 * 15)
v = 29800(3.31)^(-0.9)
Using a calculator, we can evaluate the exponential part of the equation:
v ≈ 29800(0.437)
v ≈ 13023.8
Rounding to the nearest whole number, the value of the car when it is 15 years old is 13024.
To find the value of the car when it is 15 years old, you can substitute the value of x, which is 15, into the given formula:
v = 29800(3.31)^(-0.06x)
Substituting x = 15:
v = 29800(3.31)^(-0.06 * 15)
Now, let's simplify the expression inside the parentheses:
-0.06 * 15 = -0.9
v = 29800(3.31)^-0.9
To evaluate (3.31)^-0.9, you can use a calculator or a mathematical software.
Using a calculator, raise 3.31 to the power of -0.9:
(3.31)^-0.9 ≈ 0.53578067
Now, substitute this value back into the equation:
v ≈ 29800 * 0.53578067
v ≈ 15984.557836
Since we need to round to the nearest whole number, the value of the car when it is 15 years old is approximately 15985.
We know what the value of x is: 15. So, just plug in the value of x. You can put it into a calculator and round.
By the way, in case you don't know, to "plug in a value" means to substitute in the value.