What’s the area? Please help

You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod

lorasvet [3.4K]

Answer:

a. $y=830*(0.87)^x$

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

$13\%=\frac{13}{100}=0.13$

Upon substituting our given values in exponential decay function we will get

$y=830*(1-0.13)^x$

$y=830*(0.87)^x$

Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

$y=830*(0.87)^2$

$y=830*0.7569$

$y=628.227\approx 628.23$

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be $\frac{830}{2}=415$ .

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

$415=830*(0.87)^x$

Upon dividing both sides of our equation by 830 we will get,

$\frac{415}{830}=\frac{830*(0.87)^x}{830}$

$0.5=0.87^x$

Let us take natural log of both sides of our equation.

$ln(0.5)=ln(0.87^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

$\frac{-0.6931471805599}{-0.139262067}=x$

$x=4.977286\approx 4.98$

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

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Write an equation to represent the following statement.<br> The sum of j and 47 is 55<br> .

scZoUnD [109]

Answer:

j + 47 = 53

Step-by-step explanation:

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Determine the term life insurance amount per thousand on a 23-year-old male for a 5-year policy given that the face value of the

CaHeK987 [17]

Answer:

$2.62

Step-by-step explanation:

The rate per thousand is ...

... (premium amount)/(number of thousands of face value)

... = $397.26/151.625 ≈ $2.62

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Find the slope of the line that would pass

Leno4ka [110]

Answer:

10

Step-by-step explanation:

Here we go!

Slope Formula:

$\frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} }$

What we know: (-4, -52) and (-1, -22)

Plug in the numbers!

$\frac{ - 52 - ( - 22)}{ - 4 - ( - 1)}$

Fix it!

$\frac{ - 52 + 22}{ - 4 + 1}$

Add

$\frac{ - 30}{ - 3}$

Divide

(negative divided by a negative is a positive!!)

Slope is 10

Hope this helps!

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2 years ago

What is the rate of change.

Finger [1]

Answer:

-1

Step-by-step explanation:

Over 12 on the x axis it goes down 12 on the y axis so the rate of change is -1

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3 years ago