Question

The graph of y=-3x+2 intersects the graph of an exponential function at (-1,5). Which of the following could be the

exponential function?

Answer 1

`y=10(2)^(x)`

Explanation:

Given:

The graph of
`y=-3x+2` intersects the exponential function at
`(-1,5)`.

So, the point
`(-1,5)` must also lie on the exponential function.

Let us check each option for
`y` value at
`x = -1`.

The option that gives
`y= 5` is the correct option.

Option 1:

`y=10(2)^(x)\\y=10(2)^(-1)\\y=10* (1)/(2)=(10)/(2)=5`

Option 2:

`y=10(0.5)^(x)\\y=10(0.5)^(-1)\\y=10* (1)/(0.5)=(10)/(0.5)=20`

Option 3:

`y=5^(x)\\y=5^(-1)\\y=(1)/(5)=0.2`

Option 4:

`y=5(2)^(x)\\y=5(2)^(-1)\\y=5* (1)/(2)=(5)/(2)=2.5`

Therefore, only option 1 gives 5 for
`y` when
`x=-1`

So, the correct option is
`y=10(2)^(x)`