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2 years ago

What is the range of the function f(x) = -2|x + 1|?

Mathematics

1 answer:

yanalaym [24]2 years ago

7 0

Answer:

obviously, it's at least -∞

since -2|x+1| can't be positive, we consider max(f(x)) as 0

so the range is

(-∞,0]

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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

A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were defective. A store clerk

aalyn [17]

Answer:

A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were defective. A store clerk generates random numbers to simulate a random sample of this shipment. The clerk lets the numbers 1 through 300 represent defective MP3 players, and the numbers 301 through 5,000 represent working MP3 players. The results are given.

948 628 87 4,987 938 468 3,589 298 2,459 2,286

Based on this sample, how many of the MP3 players might the clerk predict would be defective?

The manager would expect

defective players in the shipment.

6 0

2 years ago

Which machine would you use to pry a heavy rock from the ground

Sergio [31]

A lever is a simple machine that helps move or pry a rock from the ground.

5 0

3 years ago

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There are a total of 63 bikes at a sports shop. If 18 bikes are blue, what is the ratio of blue bikes to black bikes?

prohojiy [21]

Answer:

45 to 18 it's easy

Step-by-step explanation:

subtract 18 from 63 and there is your ratio

3 0

3 years ago

4. If you toss a fair coin 10 times and get heads each time, what is the probability that it will

svlad2 [7]

There’s a 5% chance

8 0

3 years ago