Question

All of these equations are EXPONENTIAL. Use example 2 on the first page to help you. What are the values for a and b in the form=⋅for this table?

Answer 1

a = 1

b = 3

Given:

`y=ab^x`

Let us try to solve for the values of a and b from the given table,

First, let us choose one pair of x and y values. To make it easier, let us choose x=0 and y=1.

Substitute these values to the equation.

`\begin{gathered} y=ab^x \\ (1)=ab^((0)) \\ \end{gathered}`

Now, remember that any number that is raised to an exponent of zero will equate to one

`\begin{gathered} 1=ab^0 \\ 1=a(1) \\ a=1 \end{gathered}`

Now that we got the value of a=1, let us choose another pair of x and y values to substitute in the equation along with the a value that we got.

This time, let us choose x=1 and y=3

`\begin{gathered} y=ab^x \\ 3=1b^1 \\ 3=b \end{gathered}`

Therefore, b=3.

To check, let us try putting an x-value that is on the table and see if we can get the right y-value

Let's say x = 4

`\begin{gathered} y=(1)(3)^x \\ y=3^x \\ y=3^4 \\ y=81 \end{gathered}`

Since we got the right y-value according to the table, we are now really sure that a=1 and b=3