Question

What is the exponential function in figure ?

Answer 1

D

Explanation:

The standard form of an exponential function is

y = a
`b^(x)`

Using points from the graph to find a and b

Using (0, 6 ), then

6 = a
`b^(0)` = a × 1 ⇒ a = 6

Using (1, 3 ), then

3 = 6
`b^(1)` ⇒ b =
`(3)/(6)` =
`(1)/(2)`

The exponential function is

f(x) = 6
`((1)/(2)) ^(x)` → D

Answer 2

D

Explanation:

I see the curve given crosses the point (1,3).

So let's check and see which of the given equations is satisfied by that point.

Checking choice A:

`y=2((1)/(4))^x` with (x,y)=(1,3):

`3=2((1)/(4))^1`

`3=2((1)/(4))`

`3=(1)/(2)`

So choice A is not right.

Checking choice B:

`y=2((1)/(2))^x` with (x,y)=(1,3):

`3=2((1)/(2))^1`

`3=2((1)/(2))`

`3=1`

So choice B is not right.

Checking choice C:

`y=6((1)/(4))^x` with (x,y)=(1,3):

`3=6((1)/(4))^1`

`3=6((1)/(4))`

`3=(3)/(2)`

So choice C is not right.

Checking choice D:

`y=6((1)/(2))^x` with (x,y)=(1,3):

`3=6((1)/(2))^1`

`3=6((1)/(2))`

`3=3`

So choice D is the only choice that would contain the point (1,3) when graphed.

So choice C is not right.