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2 years ago

What is the average rate of change of f over the interval -4≤x≤5

Mathematics

1 answer:

Ira Lisetskai [31]2 years ago

3 0

The average rate of change over the interval is 2/9

<h3>How to determine the average rate of change?</h3>

The interval is given as:

-4 ≤ x ≤ 5

From the table, we have:

f(5) = 4

f(-4) = 2

The average rate of change is then calculated as:

$m = \frac{f(5) - f(-4)}{5 --4}$

This gives

$m = \frac{4 - 2}{5 +4}$

Evaluate

$m = \frac{2}{9}$

Hence, the average rate of change over the interval is 2/9

Read more about average rate of change at:

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2 years ago

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3 years ago

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

Hi I really need help

denis-greek [22]

To solve this, you can first solve each expression:

35 / 6 = 5.83333

5 + 3/10 = 5.3

5 = 5

35 / 10 = 3.5

15 / 5 = 5

5 + 5/6 = 5.8333333

3 = 3

10 * 1/2 = 5

So, the tiles of 5, 15*1/5, and 10*1/2 all equal 5.

The tiles of 35/6 and 5+5/6 equal 5.83333.

The remaining tiles to not have matches.

4 0

4 years ago

Read 2 more answers