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

Answer:

$b = 3$

The value of y triples

Step-by-step explanation:

Given:

$\begin{array}{cccccc}x & {-2} & {-1} & {0} & {1} & {2} \ \\ y & {\frac{2}{9}} & {\frac{2}{3}} & {2} & {6} & {18} \ \end{array}$

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

$3 = b$

$b = 3$