Mathematics, 20.09.2019 11:10 snoodledoodlebop

a motorcycle cost $12,000 when it was purchased. the value of a motorcycle decreases by 6% each year. find the rate of decay each month and select the correct answer below.
−0.005143%
−0.5143%
−0.005%
−0.5%

Answers: 1

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If the rate of decay is 6% per year, that means the motorcycle retains 93% of its value every year. Because there are 12 months in a year, you can use the following equation:
x^12 = 0.94,
where x = the rate of decay each month, 12 = the number of months, and 0.94 = the retained value each year. Next, set a logarithmic function on each side as such:
LOG(x^12) = LOG(0.94)
When applying log functions, exponentials (like the 12 in the equation) are moved outside of the function like so:
LOG(x^12) = 12(LOG(x))
Therefore,
12(LOG(x)) = LOG(0.94) = -0.0268721464
When you divide both sides by 12, the equation becomes
LOG(x) = -0.00223934553
Finally, remove the LOG from the left side by applying both sides of the each by 10^() as such:
10^(LOG(X)) = 10^(-0.00223934553)
X = 0.994856987
Therefore, the motorcycle retains that 0.994856987 of its value every year.
1 - 0.994856987 = 0.005143
Expressed as a percentage, this value is 0.5143013%

Answer from: coolcat3190

The rate of decay each month is given by 0.5143% and this can be determined by forming the expression from the given data.

Given :

A motorcycle cost $12,000 when it was purchased.The value of a motorcycle decreases by 6% each year.

There are 12 months in a year then the value motorcycle retains every year is:

$x^{12}=0.94$

Now, take the log on both sides in the above equation.

$\rm logx^{12}=log(0.94)$

12 log x = log(0.94)

Now, divide log(0.94) by 12 in the above expression.

$\rm log x = \dfrac{log(0.94)}{12}$

log x = -0.00223934553

$x = 10^{-0.00223934553}$

x = 0.994856987

Now, to determine the rate of decay:

= (1 - x)100

= (1 - 0.994856987)100

= (0.005143)100

= 0.5143%

Therefore, the correct option is B).

For more information, refer to the link given below:

link

Answer from: Quest

139 divided by a number

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.

f(-x) = (-x)^2 - (-x) + 8

= x^2 + x +8

the resulting function is not identical to the original one;

f(-x) ≠ f(x)

therefore, f(x) is not an even function

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