a Enter the data into a graphing calculator, then use the Sine Regression option.
B
b Evaluate the model found in Part A with t=12.
A
a N=3.68sin(0.776t-0.70)+20.4
B
b ≈ 23 100
Practice makes perfect
a We are given a table which shows the number of employees N (in thousands) at a sporting goods company for 11 years. We want to model the number of employees N as a function of years t.
t
1
2
3
4
5
6
N
20.8
22.7
24.6
23.2
20
17.5
t
7
8
9
10
11
12
N
16.7
17.8
21
22
24.1
To create the function model, we will use a graphing calculator. Let's begin by drawing a scatter plot. We will do it by pushing the STAT button and choosing the first option Edit. Then we can enter the values. The first column represents the years and the second one represents the number of employees.
Having entered the values, we can plot them by pushing the 2nd button and the Y= button. Then, we will choose one of the plot types from the list. Let's turn the plot ON, choose the type to be a scatter plot, and assign L1 and L2 as XList and Ylist.
Now we will push the ZOOM button, and then choose the ninth option ZoomStat. The scatter plot of the data appears.
Looking at the plot, the curve appears sinusoidal. Therefore, we can perform a sinusoidal regression. By pushing the STAT button, we will go to CALC and choose option C, SinReg.
Before we perform the regression, we will store the function so that we will be able to draw it later. Let's go to the fifth row, StoreRegEQ, and press VARS. After that, we will go to Y-VARS, choose the first option, Function, and choose one of the functions to store our equation.
Now we can perform the regression.
As we drew the scatter plot, we can also draw the function.
The model seems to be a good approximation. Before we summarize our findings, let's round the SinReg values to the nearest hundredth.
N=3.68sin(0.776t-0.70)+20.4
b Now, we can use the model found in Part A to predict the number of employees at the company in the 12th year.
N=3.68sin(0.776t-0.70)+20.4
To do this, we will evaluate this function for t= 12. Let's do it!
