Question

Given two functions

$f\left(x\right)=2x+100$

$g\left(x\right)=3^x$

Calculate at what minimum integral value of $x$, $g\left(x\right)>f\left(x\right)$.

• A. $5$
• B. $3$
• C. $4$
• D. $6$

Answer 1

Answer: (A)

$5$

$f\left(x\right)=2x+100$

$g\left(x\right)=3^x$

Now,

$f\left(1\right)=102,f\left(2\right)=104,f\left(3\right)=106,f\left(4\right)=108,f\left(5\right)=110$

$g\left(1\right)=3,g\left(2\right)=9,f\left(3\right)=27,g\left(4\right)=81,g\left(5\right)=243$

$g\left(5\right)>f\left(5\right)$

Thus at $x=5$

$g\left(x\right)>f\left(x\right)$

$x=5$ is the answer.