Question

The table below shows some values of f(x) and g(x) for different values of x: x f(x) = 2x + 24 g(x) = 5(0.5)x −2 20 −1 0 5 1 2.5 2 28 complete the chart and determine the solution of the equation f(x) = g(x). a x = −2 b x = −1 c x = 1 d x = 20

Answer 1

answer is A

Explanation:

Answer 2

for
`x=-2`


`f(-2) = 2(-2) + 24 = -4 + 24 = 20`

`g(-2)=5 (0.5)^(-2)=20`

for
`x=-1`


`f(-1)=2(-1)+24=22`

`g(-1)=5 (0.5)^(-1) =10`

for
`x=0`


`f(0)=2(0)+24=24`

`g(0)=5 (0.5)^(0)=5`

for
`x=1`


`f(1)=2(1)+24=26`

`g(1)=5 (0.5)^(1)=2.5`

If we continue to substitute the value of x, we'll find that f(x) will increase with the constant rate of 2 for every x, while g(x) will exponentially decrease.

Notice that for the value of
`x=-2` we have
`f(x)=g(x)` hence, the answer is A