Mathematics, 29.11.2019 08:31 maddieg5585

An equation for the depreciation of a car is given by y = a(1 – r)t , where y = current value of the car, a = original cost, r = rate of depreciation, and t = time, in years. the value of a car is half what it originally cost. the rate of depreciation is 10%. approximately how old is the car?

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Answer from: imstoopid69

A(1 – r)t , where y = current value of the car,

Answer from: acrespo3425

The car is 6.5788 years old.

Step-by-step explanation:

The key to solve the problem is in the following sentence: "The value of a car is half what it originally cost". Keep in mind that is the current value and is the original cost. It means that is half of : $y=\frac{A}{2}$ .

It is assumed that the rate of depreciation is annually and its value is $10\%$ . Remember that $10\%$ equals 0.1 , so r=0.1 .

For finding the value of , you must replace the values of and in the depreciation formula:

$y=A\cdot (1-r)^t$

$\frac{A}{2}=A\cdot (1-0.1)^t$

After cancelling the variable the equation would be:

$\frac{1}{2}=(0.9)^t$

For finding the value of you must apply natural algorithm in both sides:

$ln\bigg( \frac{1}{2}\bigg) =ln[(0.9)^t]$

$ln(0.5)=t\cdot ln(0.9)$

$t=\frac{ln(0.5)}{ln(0.9)}$

t=6.5788

The previous value can be split in two parts: 6+0.5788 . The first part refers to years and the second part can be converted to months by multiplying the total months in a year () by 0.5788 .

$months=12\times 0.5788=6.9456$

Thus, the car is 6.5788 years old (which is approximately 6 years and almost 7 months).

Answer from: Quest

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

Answer from: Quest

step-by-step explanation:

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