# How do you get these two equations into one equation?

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Find an exponential function that passes through each pair of points. Write your answer like y=a(b)^x

The ordered pairs are: (1,7.5) and (3,16.875)

What are the equations to both of them? I want to know if I did it right.

Find an exponential function that passes through each pair of points. Write your answer like y=a(b)^x

The ordered pairs are: (1,7.5) and (3,16.875)

What are the equations to both of them? I want to know if I did it right.

##### 1 Answer

#### Explanation:

The problem tells us that our function will look like this:

#y = a*b^x#

So, if we can solve for

So, let's plug in the two coordinates and see what we get:

First, the point

#(color(red)1, color(blue)7.5)#

#color(blue)7.5 = a * b^color(red)1#

#color(blue)7.5 = ab# Next, the point

#(color(red)3, color(blue)16.875)#

#color(blue)16.875 = a * b^color(red)3#

#color(blue)16.875 = ab^3#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This gives us a system of equations in terms of

#7.5 = ab " "" "and" "" "16.875 = ab^3#

Since

#16.875/7.5 = (ab^3)/(ab)#

#2.25 = (cancela * cancelb * b^2)/(cancela * cancelb)#

#2.25 = b^2#

#+- 1.5 = b#

And since

#b = 1.5#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now that we have solved for

#7.5 = ab#

#7.5 = a(color(orange)1.5)#

#5 = a#

So

#y = 5 * 1.5^x#

*Final Answer*