Question

FAN AND MEDAL

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)?
x = -2

x = -1

x = 1

x = 20

Answer 1

$$
f(x)=2x + 24 \\
g(x) = 5(0.5)x
$$
For x=-1
$$
f(-1)=2(-1)+24=-2+24=22\\
g(-1)=5(0.5)(-1)=-2.5
$$
Similarly for x=0
$$
f(0)=?\\
g(0)=?
$$
And so on...

Now for g(x)=f(x)
$$
2x + 24=5(0.5)x\\
2x-5(0.5)x=-24\\
x(2-2.5)=-24\\
x=-24/-1.5\\
=24/.5=48
$$

Does this help?

Answer 2

I'm confused.
What exactly does 24/.5 = 48 tell me ?

Answer 3

$$
x=24/.5=\cfrac{24}{0.5}=\cfrac{24}{\frac{1}{2}}=24\times2=48\\
$$
At this value of x
$$
g(x)=f(x)
$$
Because,
$$
g(48)=5(0.5)(48)=120\\
f(48) = 2(48) + 24=120
$$
So
$$
g(48)=f(48)
$$

Answer 4

So x=1 ?

Answer 5

no, x=48.

Answer 6

f(-2) = 2(-2) + 24

f(-2) = 20

g(-2) = 5*4

g(-2) = 20

Its x = -2 because THEY BOTH EQUAL 20

Answer 7

so its a or what