Question

[Exponential] |x|-2|-1|0|1|2| |y|2/9|2/3|2|6|18| When the x-value increases by 1, the y-value ________ (b-value)

Answer 1

`b = 3`

The value of y triples

Explanation:

Given:

`\begin{array}{cccccc}x & {-2} & {-1} & {0} & {1} & {2} \ \\ y & {(2)/(9)} & {(2)/(3)} & {2} & {6} & {18} \ \end{array}`

Required

Determine b value

An exponential equation is:

`y = ab^x`

When
`x = 0; y =2`

So:

`y = ab^x`

`2 = a * b^0`

`2 = a`

`a = 2`

When
`x = 2; y = 18`

So:

`18 = a * b^2`

Substitute 2 for a

`18 = 2 * b^2`

Divide by 2

`9 = b^2`

Take positive square roots of both sides

`3 = b`

`b = 3`