Question

which function is represented in the graph ?- y = 3 ( .5x )- y = 3 (2x )- y = 2 ( 3x ) - y = 2 ( .5x )

Answer 1

`y=3(2)^x`

1) First of all, note that the direction of a curve in an exponential function depends on the factor.

2) As we can see the curve is from the left to right, so this is an increasing exponential function and the factor has to be greater than 1.

3) As we can see the curve hits the graph at the point (0,3) so we can tell the initial value is 3. And picking another point (1,6) We can find the elements of this exponential function by doing this:

`\begin{gathered} y=ab^x \\ 3=ab^0 \\ a=3 \\ ----- \\ (1,6) \\ 6=3(b)^1 \\ 3b=6 \\ (3b)/(3)=(6)/(3) \\ b=2 \end{gathered}`

Thus, the answer is:

`y=3(2)^(x)`