Question

An exponential function has the equation y = (0.5)^x-1. Four points from a different function as shown in the table. For what values of x will two functions be equal?

Answer 1

The analysis above, it seems that the correct answer is C) x=0,1, as both

x=0 and x=1 satisfy the equation. Therefore ,C) x=0,1 is correct.

To find the values of x for which the two functions are equal, set their expressions equal to each other and solve for x:

y=
`(0.5) ^(x)` − 1

Let
`y_(1)` be the value of the exponential function and
`y_(2)` be the value from the other function.

So:

`(0.5) ^(x)`− 1 =
`y_(2)`

Now, examine the given choices:

A) x=0: Plug in x=0 into the equation to see if both sides are equal:

`(0.5)^0` − 1 = 1 − 1 =0

This is not equal to any of the values for
`y_{2`

B) x=−1,0: Plug in x=−1 and x=0 into the equation:

For x=−1:
`(0.5)^ −1`=2− 1 = 1

For x=0:
`(0.5)^−0`=1 − 1 = 0

So, x=0 is a solution.

C) x=0,1: Plug in x=0 and x=1 into the equation

For
`(0.5)^-0` −1=1−1=0

For x=
`(0.5)^−1\\` −1=0.5−1=−0.5

So, x=0 is a solution.

D) The functions are never equal.

From the analysis above, it seems that the correct answer is C) x=0,1, as both x=0 and x=1 satisfy the equation .

Question

An exponential function has the equation y=(0.5)^x-1. Four points from a different function are shown in the table. For what values of x will the two functions be equal? -

A) x=0

B) x=-1,0

C) x=0,1

D) The functions are never equal.