Question

Please Help - Easy Question Algebra 2.

Answer 1

The function is exponential

Its equation is
`y = (7)/(3) \cdot((1)/(3) )^x`

Explanation:

We can see that, as x increases by a constant y increases by a factor of
`(1)/(3)`

So the table represents an exponential equation

The form of the equation is
`a\cdot((1)/(3))^(x)`

All we have to do is determine a

Take the entry for x = 0

At x = 0, the equation becomes y =
`a\cdot((1)/(3)) ^ 0`

Any number raised to the power 0 is 1

So at
`x = 0, y = a\cdot1 = a`

But we know the y value at x = 0 is
`(7)/(3)`

So
`a = (7)/(3)`

The equation of the function is

`y = (7)/(3) \cdot((1)/(3) )^x`

We can verify by plugging in a few values for x into the above equation and seeing if the corresponding calculated values concur with the one in the table

For
`x = - 1, y = (7)/(3)\cdot ((1)/(3))^(-1) = (7)/(3)\cdot 3 = 7`

You can try the other x values and see that computed and given y values concur