Question

graph the functions and approximate an x value in which the exponential function surpases the polynomial function. f(x)=4^x g(x)= 4x^2

Answer 1

check the picture below.

notice, 4ˣ surpasses 4x² at roughly (2,16), so any points above that will do.

Answer 2

The value of x is 2.

Explanation:

Given functions,

`f(x) = 4^x-----(1)`

`g(x)=4x^2-----(2)`

Equation (1) is an exponential growth function, having y-intercept (0, 1) and horizontal asymptote x-axis, ( shown in the below graph ),

Equation (2), is an upward parabola having vertex (0,0),

By the below graph,

Equation (1) exceed the equation (2) at (2, 16),

Hence, the value of x in which the exponential function surpases the polynomial function ( equation (2) ) is 2.