Question

I need algebra help.....

Answer 1

`y=4(3)^x`

Explanation:

From the table given in the question,

x y Difference Ratio

1 12 - -

2 36 36-12 = 24
`(36)/(12)=3`

3 108 108-36 = 72
`(108)/(36)=3`

4 324 324-108 = 216
`(324)/(108)=3`

5 972 972-324 = 648
`(648)/(216)=3`

There is a common ratio of 3 in each successive term.

Therefore, data given in the table will represent an exponential function.

`y=a(b)^x`

For a point
`(1, 12),`

`12=a(b)^1`

`ab=12` ------(1)

For another point of the table
`(2,36)`,

`36=a(b)^2`

`ab^2=36` --------(2)

Equation (2) divided by equation (1)

`(ab^2)/(ab)=(36)/(12)`

`b=3`

From equation (1),

`3a=12`

`a=4`

Therefore, exponential function will be,

`y=4(3)^x`