Question

Use a graphing calculator to find the approximate solution to 3x^2 -4=2^x to 2?decimal places

Answer 1

To answer this question we will graph the function:

`f(x)=3x^2-4-2^x.`

Notice that:

`f(x)=0\text{ if and only if }3x^2-4=2^x.`

Therefore the x-coordinates of the x-intercepts will be solutions to the given equation.

The graph of f(x) is:

From the graph we get that the approximate solutions to the given equation are:

`x\approx-1.22,x\approx1.51,\text{ and }x\approx7.27.`

Answer: Second option.