What is the slope of-5y=2x

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

3 years ago

What number has the same value as 40 tens

MariettaO [177]

Answer: 400 because 40 multiplied by ten equals 400 hundred, so basically it's just 40 multiplied by 10.

6 0

2 years ago

Which type of transformation maps triangle GFH onto triangle G'F'H'?

lions [1.4K]

Answer:

rotation

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is 29/33 in simplest form

Oduvanchick [21]

29/33 is already in simplest fraction form

29 is a prime number and cannot be simplified more

6 0

2 years ago

Read 2 more answers

6. Carla runs 3 miles in 30 minutes.

NARA [144]

Answer:

Carla ran 0.1 miles per minute.

Step-by-step explanation:

To solve this, we need to use the distance formula.

The formula is d=rt, where d is the distance traveled, r is the rate in which the distance is traveled, and t is the amount of time it took to go that distance. So lets plug it all in.

d=rt

3=(r)(30)

Now, we need to do the inverse of multiplying 30 to both sides, which would be the same as dividing by 30 on both sides.

3/30=(r)(30/30)

0.1=r

The rate is 0.1. Carla ran 0.1 miles per minute.

3 0

2 years ago