A linear function is given by f(x) = 2x + 10, and an exponential function is given by g(x) = 2^x. For positive integer values of x, what…

Compare the two functions at positive integers. At $x=1$: $g=2$ and $f=12$. At $x=2$: $g=4$ and $f=14$. At $x=3$: $g=8$ and $f=16$. At $x=4$: $g=16$ and $f=18$, so $f$ is still larger. At $x=5$: $g=32$ and $f=20$, so $g$ is finally larger. The smallest such $x$ is $5$, choice A. Choice B ($4$) is the last value where the linear function is still larger. Choices C ($3$) and D ($6$) are not the first crossing. Exponential growth eventually overtakes linear growth, even from a lower starting point.