Write an exponential function for the following set of data

Question

X: -2 -1  0     1     2

Y: 5 25 125 625 3125

Answer 1

What we have here is 5^x, as every exponential value is a multiplication of 5. That means our basic equation looks like:

y = 5^x

Now we need to shift it based on the x values giving us the y. For example, 5¹ is the same as 5. This means we need:

x - 2 = 1

Add 2 to both sides:

x = 3

 

SO our final equation looks like:

y = 5^x+3

Answer 2

Exponential functions are ones which model growth which is proportional to the current value of the function.  In other words, if you look at the y values for two x values, the proportion between the y values is determined by the difference between the x values.

 

That said, to find a function for some set of data like this, we just have to find a factor B which is multiplied on each time x increases, and the function will take the exponential form with base B:

y = A⋅B^x

 

In this case, each y value is 5 times the previous y value, so we can think about the function in this way:

y = A⋅5^x

 

Now we just need to find an A that works for our data.  Plugging in x=0 will give y=125, so we can solve for A:

y = A⋅5^x

125 = A⋅5⁰

125 = A⋅1

125 = A

 

So the function can be written as y = 125⋅5^x