Solving Exponential Equations

To solve the exponential equation by graphing, we first have to create two functions. Each side of the given equation will become a function. $$\begin{array}{r}4e^{0.1x}=60\Rightarrow \begin{array}{l}y=4e^{0.1x}\\ y=60\end{array}\end{array}$$ Now, we want to draw these graphs using a calculator. We can do this by pressing the $\boxed{\text{Y=}}$ button and typing the equations in the first two rows.

Before we graph these functions, notice that the second function is a horizontal line at $y=60,$ so we will not be able to see this in the standard viewing window. Also, the exponent of $e$ is $0.1x,$ so the function will grow very slowly. In order to accommodate these issues, we should change the viewing window.

There is one point of intersection of these graphs. To find this point we can use the intersect option, which we get by pushing $\boxed{2\text{nd}}$ and $\boxed{\text{TRACE}}.$ Now, we select both graphs and provide the calculator with a guess as to where the intersection might be.

The solution to the equation is $x\approx 27.1.$