PLEASE HELP ME THIS IS DUE ASAP!!! I will mark brainliest if right!!! Explain!

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.

5 0

3 years ago

The graph of f(x) = x2 + x - 6 is shown below.

guapka [62]

Answer:

the solutions of a function are the points where for some value of x the function becomes zero

thus the solns for this graph would be

that's option 1.

3 0

2 years ago

Part A: Rhett made $250 washing cars with his mobile car wash company. He charges $70 per car and earned $50 in tips. Write an e

Natasha2012 [34]

Answer:

250=70x+50

Step-by-step explanation:

5 0

3 years ago

One garden had 5 times as many raspberry bushes as a second garden. After 22 bushes are transplanted from the first garden to th

Aleonysh [2.5K]

Let the number of raspberry bushes in one garden = x

And the number of raspberry bushes in second garden = y

Garden one has 5 times as many raspberry bushes as second garden,

So the equation will be,

x = 5y -------(1)

If 22 bushes were transplanted from garden one to the second, number of bushes in both the garden becomes same,

Therefore, (x - 22) = (y + 22)

x - y = 22 + 22

x - y = 44 ------(2)

Substitute the value of x from equation (1) to equation (2)

5y - y = 44

4y = 44

y = 11

Substitute the value of 'y' in equation (1),

x = 5(11)

x = 55

Therefore, Number of bushes in garden one were 55 and in second garden 11 originally.

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5 0

3 years ago

HELP MEEEEEEEEEEEEEEEE

Monica [59]

Answer:

Lest then 5/8

Step-by-step explanation:

Lest then 5/8

5 0

2 years ago