# Exponential and Logistic Modeling on a Graphing Calculator

## Key Questions

• I don't think you can make a model with the $e$ or the two $k$ and the $t$. However, you can make a $y = a {b}^{x}$ model using the Exponential Regression key. To use this, go to STAT$\to$CALC$\to$and scroll down until you see "ExpReg".

Then, if you have data entered into your STAT key, then you'll get a model for that.

Hope that helps :)

• I assume you mean the "A" as in the initial value of $y = A {e}^{r t}$? $y$-intercept

The "a" value occurs at $t = 0$, so ${e}^{0} = 1$, therefore $y = A$ is $\left(0 , A\right)$, the $y$-intercept.

• Consider the exponential function $f \left(x\right) = {a}^{k x}$, where $a$ and $k$ are constant, $a , k \in \mathbb{R}$.

I prepared a dynamic plot that can be used to study the properties of the exponential function as $a$ and $k$ take various values.

Please use the provided sliders to change the values of the parameters $a$ and $k$ and see what happens to the graph of the function.

Pay particular attention to the cases when $0 < a < 1$ and $a > 1$. For each of these cases, see what happens when $k < 0$ and $k > 0$.