Question

Find the missing values for the exponential function represented by the table below.

x y
-2 7
-1 10.5
0 15.75
1
2

Answer 1

x y

-2 7

-1 10.5

0 15.75

1 23.625

2 35.4375

Explanation:

The general equation of the exponential function is
`y=ab^x`.

We know from our table that when
`x=0`,
`y=15.75`. Let's replace those values in our equation:

`y=ab^x`

`15.75=ab^0`

Remember that
`b^0=1`, so:

`15.75=a(1)`

`15.75=a`

`a=15.75`

We also know from our table that when
`x=-1`,
`y=10.5`. Let's replace the values again:

`y=ab^x`

`10.5=ab^(-1)`

But we now know that
`a=15.75`, so let's replace that value as well:

`10.5=15.75b^(-1)`

Remember that
`b^(-1)=(1)/(b)`, so:

`10.5=(15.75)/(b)`

`10.5b=15.75`

`b=(15.75)/(10.5)`

`b=1.5`

Now, we can put it all together to complete our exponential function:

`y=ab^x`

`y=15.75(1.5)^x`

To find the missing values, we just need to evaluate our function at
`x=1` and
`x=2`:

- For
`x=1`

`y=15.75(1.5)^x`

`y=15.75(1.5)^1`

`y=23.625`

- For
`x=2`

`y=15.75(1.5)^x`

`y=15.75(1.5)^2`

`y=35.4375`