Question

Which exponential function goes through the points (1, 16) and (4, 128)?

Answer 1

F(x)=8(2)x

Explanation:

Answer 2

Here is the complete question (attachment).

The function which represent the given points are
`f(x)=8(2)^(x)`

Explanation:

We know that a general exponential function is like,
`y=a(b)^(x)`

We can find the answer by hit and trial method by plugging the values of
`(x,y)` coordinates.

Here we are going to solve this with the above general formula.

So as the points are
`(1,16)` then for
`x=1,\ y=16`

Can be arranged in terms of the general equation.

`ab^1=16`...equation(1) and
`ab^4=128`...equation(2)

`a* b=16, then\ a=(16)/(a)`

Plugging the values in equation 2.

We have

`(16)/(b) b^4=128,16* b^3=128,b=\sqrt[3]{(128)/(16)} =\sqrt[3]{8}=2`

Plugging
`b=2` in equation 1.

We have
`a=(16)/(b) =(16)/(2) =8`

Comparing with the general equation of exponential
`a=8` and
`b=2`

So the function which depicts the above points =
`y=8(2)^x`

From theoption we have B as the correct answer.