Chapter 3, Problem 1RE

In Exercises 1-6, match each equation in column A with the most appropriate graph in column B Column B

Column A

$P\left(t\right)=50e^{0.03t}$

To determine

The correct match for the graph of the function $P\left(t\right)=50e^{0.03t}$ from the provided graph.

Answer to Problem 1RE

Solution:

The correct match for the graph of the function $P\left(t\right)=50e^{0.03t}$ is (b).

Explanation of Solution

Given information:

The provided graphs:

Consider the function,

$P\left(t\right)=50e^{0.03t}$

At $t=-40$.

$\begin{array}{c}P\left(-40\right)=50e^{0.03\left(-40\right)}\\ =15.05\end{array}$

At $t=-20$.

$\begin{array}{c}P\left(-20\right)=50e^{0.03\left(-20\right)}\\ =27.44\end{array}$

At $t=0$.

$\begin{array}{c}P\left(0\right)=50e^{0.03\left(0\right)}\\ =50\end{array}$

At $t=20$.

$\begin{array}{c}P\left(20\right)=50e^{0.03\left(20\right)}\\ =91.10\end{array}$

At $t=40$.

$\begin{array}{c}P\left(40\right)=50e^{0.03\left(40\right)}\\ =166\end{array}$

Now, the table for ordered pair $\left(t,P\left(t\right)\right)$ for the function $P\left(t\right)=50e^{0.03t}$ is shown below:

$\begin{array}{cc}t& P\left(x\right)\\ -40& 15.05\\ -20& 27.44\\ 0& 50\\ 20& 91.10\\ 40& 166\end{array}$

So, the resulting graph is,

This is identical to the graph in part (b). Hence, the correct match is part (b).