Question

To estimate the values of \(x\) using graph of \(f(x) = {e^x}\) for which \({e^x} > 1,000,000,000\).

Short answer

The values of \(x\) for which \({e^x} > 1000000000\) are \(x > 20.723\).

Step-by-step solution

Given information

The graphs of \(f(x) = {e^x}\) for which, \({e^x} > 1,000,000,000\).

 Step 2: Use the graph of a function

The graph of a function\(f\)is the set of all points in the plane of the form\((x,f(x))\).

Draw the graph of the function \(f(x) = {e^x}\)

The graph of the function \(f(x) = {e^x}\)is shown in the Figure 1.

From Figure1, observe that the intersection point of the curve with the line\(y = 1000000000\)is\((20.723,1000000000)\).

Also note that function is increasing for all values of\(x\).

Thus,\({e^x}\)will take values greater than 1000000000 when\(x > 20.723\).

Hence \({e^x} > 1000000000\) for all values of \(x\) such that \(x > 20.723\).