1 Answer

Marine · Answer 1 · 2019-02-05T06:34:41+0000

We have to functions, namely:

$f(x)=200(2)^(x) \ and \ g(x)=500x+400$

So the problem is asking for the smallest positive integer for

so that

is greater than the value of
g(x)

, that is:

$f(x)\ \textgreater \ g(x) \\ \therefore 200(2)^(x)\ \textgreater \ 500x+400$

Let's solve this problem by using the trial and error method:

$for \ x=1 \\f(1)=400 \\ g(1)=900 \\ Then \ f(1) \ \textless \ g(1) \\ \\ \\ for \ x=2 \\f(2)=800 \\ g(2)=1400\\ Then \ f(2)\ \textless \ g(2) \\ \\ \\ for \ x=3 \\f(3)=1600 \\ g(3)=1900 \\ Then \ f(3)\ \textless \ g(3) \\ \\ \\ for \ x=4 \\f(4)=3200 \\ g(4)=2400 \\ \boxed{Then \ f(4)\ \textgreater \ g(4)}$

So starting

from 1 and increasing it in steps of one we find that:

f(x)>g(x)