Question

math problem

Answer 1

like a first step the form of an exponential function

\(\f(x) = b^x\)

where b>0

Answer 2

we can do it the way András did it -- we can also use this other way, by just picking 2 points, instead of many of them -- it continues as following:

so let's just pick 2 points where the line passes through -- i'm picking (0 . 1) and (3 . 8)

Answer 3

the formula we will be using is \( f(x) = Ca^x \) -- let's do (0 . 1) first
\[ f(0)=1=C a^0 \]
\[C=1\]

Answer 4

now that we know \( C=1 \) we can continue as following with (3 . 8), just as following :

\[f(3)=8=1a^3\]
\[8=a^{3}\]
\[a=\sqrt[3]{8}\]
\[a=2\]

Answer 5

now that we have all that, we can just substiture the numbers in
\[f(x)=1\left(2^x\right)\]
\[f(x)=2^x \]
and that would be our answer.