Chapter 4, Problem 6P

To determine

To find: The model of given table as power function $y=a{t}^b$ and exponential function. 1y1y3 $y=a{b}^t$ .

Answer to Problem 6P

Power Function :$y=30.477x^{-0.155}$

Exponential function: $y=44.824{\left(0.857\right)}^x$

Explanation of Solution

Given: The table shown below:-

  $\begin{array}{cc}\text{Time}& \text{Words recalled}\\ 15\text{ min}& 64.3\\ 1\text{}\text{ h}& 45.1\\ 8\text{ h}& 37.3\\ 1\text{ day}& 32.8\\ 2\text{ days}& 26.9\\ 3\text{ days}& 25.6\\ 5\text{ days}& 22.9\end{array}$

In the given table, first change all time value in days

  $\begin{array}{cc}\text{Time}& \text{Words recalled}\\ 0.01\text{ day}& 64.3\\ \text{0}\text{.042 day}& 45.1\\ 0.333\text{ day}& 37.3\\ 1\text{ day}& 32.8\\ 2\text{ days}& 26.9\\ 3\text{ days}& 25.6\\ 5\text{ days}& 22.9\end{array}$

Using table find power function and exponential function.

Using calculator the power function, $y=30.477x^{-0.155}$

The exponential function, $y=44.824{\left(0.857\right)}^x$

To determine

To plot: The scatter plot of given data and plot power function and exponential function on same graph.

Answer to Problem 6P

  

Explanation of Solution

Given: The table shown below:-

  $\begin{array}{cc}\text{Time}& \text{Words recalled}\\ 15\text{ min}& 64.3\\ 1\text{}\text{ h}& 45.1\\ 8\text{ h}& 37.3\\ 1\text{ day}& 32.8\\ 2\text{ days}& 26.9\\ 3\text{ days}& 25.6\\ 5\text{ days}& 22.9\end{array}$

Using calculator the power function, $y=30.477x^{-0.155}$

The exponential function, $y=44.824{\left(0.857\right)}^x$

Now plot the points on graph

Where, x -axis represents number of days and y -axis represents words called.

  

To determine

To plot: The scatter plot of given data and plot power function and exponential function on same graph.

Answer to Problem 6P

Power function

Explanation of Solution

Given: The table shown below:-

  $\begin{array}{cc}\text{Time}& \text{Words recalled}\\ 15\text{ min}& 64.3\\ 1\text{}\text{ h}& 45.1\\ 8\text{ h}& 37.3\\ 1\text{ day}& 32.8\\ 2\text{ days}& 26.9\\ 3\text{ days}& 25.6\\ 5\text{ days}& 22.9\end{array}$

  

According to graph, power function is better model.