Function f is an exponential function. it predicts the value of a famous painting, in thousands of dollars, as a function of the number of years since it was last purchased. what equation models this function? graph on a coordinate plane with axes labeled x and f of x. an exponential curve passes through 0 comma 8, 1 comma 10, and 2 comma 12.5. enter your answer in the box. f(x)=

or

Step-by-step explanation:

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

, ().

If you are given the intercept, then is easy to find.

It is just the coordinate of the intercept is your value for .

(Why? The intercept happens when . Replacing with 0 gives . This says when .)

So .

So our function so far looks like this:

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

Let's do this.

We are given is a point on our curve.

So when , .

Divide both sides by 8:

Reduce the fraction:

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

Let's try it.  So the last point given that we need to satisfy is .

This says when , .

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

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

The equation is .

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.