Question

How do you solve `4^x+4>=21` using a graph?

Answer 1

Solution is `x>=2.04371`

Explanation:

To solve `4^x+4>=21` using a graph, first let us create a graph by choosing different values of `x` say `-1`, `-1/2`, `0`, `1/2`, `1`, `3/2`, `2`, `5/2`, `3` and corresponding values of `4^x+4`.

These are `((-1,-1/2,0,1/2,1,3/2,2,5/2,3),(17/4,9/2,5,6,8,12,20,36,68))`

and graph appears as follows:
graph{4^x+4 [-1, 3, -5, 30]}

As is observed by zooming the graph near the place, where `4^x+4` crosses `y=21` and we find that `4^x+4>=21` for some `x` greater than `2`, say around `2.04`.

graph{4^x+4 [1.68, 2.18, 16.944, 21.32]}

Actually solution is `x>=2.04371` (using MSExcel - Goal seek).