math problem

Question

math problem

klmjnmkj · Answer

attachment

jhonyy9 · Answer

like a first step the form of an exponential function

$\f(x) = b^x$

where b>0

Florisalreadytaken · Answer

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)

Florisalreadytaken · Answer

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

Florisalreadytaken · Answer

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

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

Florisalreadytaken · Answer

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.