Question

Find an equation of g(x) from the table. I know its divided by 2 but I don't know how to write an equation for it. I know I have to use the f(x)=32 but I don't know what to write after that.
f(x)
32
16
8
4
2

Answer 1

Which table?

Answer 2

I am given a table of f(x), g(x), h(x), k(x) but I only need to write an equation for f(x) which is the numbers listed above for f(x) sorry I put g(x) on accident. I know the pattern is each number is divided by 2 so I need to write an equation for that. I just don't know what to put for division.

Answer 3

unless I put multiplied by 1/2 such as f(x)=32(1/2)^x

Answer 4

sorry
\[f(x) = 2^{x}\]

Answer 5

2^1= 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32

Answer 6

hmm.. so i don't include 32?

Answer 7

why do you need to include 32?
question requires to generate an equation that satisfy the table.

Answer 8

oh haha Ive never used or generated an equation like before from a table usually i use the number but now I know I can do that too so thanks!

Answer 9

My pleasure :)

Answer 10

to write the equation, we need to know (x, f(x) ) pairs.
Your list of numbers in the question is not enough. Are those f(x)? if so, what is x?
if the list were
x f(x)
0 32
1 16
2 8
3 4
4 2

we could write an equation.
We first find the differences between f(x) values: 16, 8, 4 ... These are not constant, so the function is not linear.

try finding the ratio between f(x) values: 16/32= 1/2, 8/16= 1/2, etc... We get a ratio of 1/2. So the function is "geometric". Expect a function of the form

f(x)= A r^x with r= 1/2
when x is 0 we want f(x)= 32. put those numbers into
\[ f(x)= A r^x \\ 32 = A \left( \frac{1}{2}\right)^0 \\ 32=A\]
and we get
\[ f(x) = 32 \left( \frac{1}{2}\right)^x\]
Of course, all of this depends on what the x values are in your table.
If we started with x=1, we would have to tweak this answer.

If we want to get cute, we can notice 32= 2^5 and (1/2)^x is 2^(-x) , so that
\[ f(x) = 32 \left( \frac{1}{2}\right)^x = 2^5 \ 2^{-x} \\ f(x)= 2^{5-x}
\]
as an alternate way to write the function.