Solving Exponential Equations

To solve the exponential equation by graphing, we first have to create two functions. Each side of the given equation will a function. $$\begin{array}{r}450e^{0.4x}=2000\Rightarrow \begin{array}{l}y=450e^{0.4x}\\ y=2000\end{array}\end{array}$$ 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 two first rows.

Before we graph these functions, notice that the second function is a horizontal line at $y=2000,$ so we will not be able to see this in the standard viewing window. In order to accommodate this issue, 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 $x\approx 3.73.$ We will check our answer by substituting $3.73$ for $x$ in the original equation. Notice that the answer that we found is an approximate value, so we may not have an identity at the end. However, we can accept an approximate result. Since we obtained a true statement, $x\approx 3.73$ is a solution to the equation.