Solve T= C(7+AB) for A

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

2 years ago

Answer the question in the picture pls WORTH 50 POINTS PLUS BRAINLIEST FOR FIRST CORRECT ANSWER

Alexus [3.1K]

Answer:

A

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−y+4≥8

Step 2: Subtract 4 from both sides.

−y+4−4≥8−4

−y≥4

Step 3: Divide both sides by -1.

−y

−1

≥

4

−1

y≤−4

5 0

2 years ago

Read 2 more answers

30 points!<br> You start at (-2, 2). You move left 3 units and right 10 units. Where do you end?

Cerrena [4.2K]

Answer:

The answer is (5, 2)

Step-by-step explanation:

I. If move left = -x

move right = +x

So -2 - 3 = -5 => move left

-5 + 10 = 5 => move right

I suggest that move left and right is x cordinate

The answer is (5,2)

Is that correct?

7 0

2 years ago

In reading class, Phillip read 38 of a book. Alicia read 58 of the same book.

Otrada [13]

Answer:

phillip

Step-by-step explanation:

because phillip read 38 books and alicia read 1 book 58 time and the reason i picked phillip cause he read different books with more pages and alicia read the same book that probably had a little bit of pages

sorry if it is wrong

5 0

1 year ago

1. Suppose you flip a penny 50 times, with 25 tosses landing heads up. What percentage of the tosses would be heads? %

Paul [167]

Answer:

50%

Step-by-step explanation:

Half of 50 is 25, so when it comes to a percent, half of 100% (50) is 50% (25)

8 0

2 years ago