[tex]f(x)=2^x[/tex]
Explanation
Step 1
[tex]1\Rightarrow2[/tex]
so
[tex]f(1)=2[/tex]
now
for the others
[tex]\begin{gathered} f(2)=4 \\ f(3)=8 \\ f(4)=16 \\ f(5)=32 \end{gathered}[/tex]
as you can see, each new term in y is 2 times the previous
then
[tex]f(x)=2^x_{^{^{}}}[/tex]
input the values to prove
[tex]\begin{gathered} f(x)=2^x \\ f(1)=2^1=2,ok \\ f(2)=2^2=4 \\ f(3)=2^3=2.2.2=8 \\ f(4)=2^4=2.2.2.2=16 \\ f(5)=2^5=2.2.2.2.2=32 \end{gathered}[/tex]
I hope this helps you
