Given a dilation around the origin, what is the scale factor K?<br><br> D o, K = (2,4) → (3,6)

Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

4 0

2 years ago

Linda watched a video. The introduction is 2 minutes, and the video is 7 minutes. What percentage of the video is the introducti

kolezko [41]

Answer:

22.222222%

Step-by-step explanation:

all together the entire video is 9 min and 2 of those are the intro so 2/9 and that as a percent is the answer

4 0

2 years ago

Read 2 more answers

Every year the Lee family has a big family dinner, and everyone brings a mug to exchange. The mugs are put on wooden hangers on

RideAnS [48]

Answer:

21 more mugs were brought this year than last year.

Step-by-step explanation:

We can solve by subtracting the initial amount of mugs from the final amount of mugs.

To find the amount of mugs hung up this year, we will use the equation: m = 12w where m = the number of mugs & w = the number of wooden hangers. The 12 represents the amount of mugs per wooden hanger.

We can plug in 3 for w since 3 wooden hangers were filled up and we would get 12(3) = m = 36 mugs

Now we subtract last year's total mugs hung up from this year's total mugs hung up.

We end up with 36 - 15 = 21

4 0

2 years ago

A line with a slope of 5 passes through the point (0,0). What is its equation in slope-intercept form?

Masja [62]

Answer:

y=5x or y=5x+0

Step-by-step explanation:

there is a slope of 5 and it has no setoff

5 0

2 years ago

Find the mean of the following data set<br> 73, 81, 51, 76, 89, 95, 88

kifflom [539]

Answer:

$mean = \frac{(73 + 81 + 51 + 76 + 89 + 95 + 88)}{7} \\ = 79$

6 0

2 years ago

Read 2 more answers

Given a dilation around the origin, what is the scale factor K? D o, K = (2,4) → (3,6)