a Begin with resizing the window by pushing WINDOW and changing the settings.
B
b Substitute the given values into the given function.
C
c How are the strengths changing according to the corresponding distances?
A
aGraph :
Distances: d ≥ 40
B
b10 Miles: 16
1 Mile: 1600 0.1 Miles: 160 000
C
c See solution.
Practice makes perfect
a We are given a function that represents the strength s of a signal at a distance of d miles from a transmitter.
s = 1600/d^2
We want to graph this function using a graphing calculator. To do so we need to rearrange our variables. We will write d as x and s as y.
s=1600/d^2 ⇔ y = 1600/x^2
Now we will resize the window by pushing WINDOW and changing the settings. We will set the window to use only the first quadrant because only the nonnegative values make sense for this case.
Now that we have set the window, we can graph our function. To do so we first press the Y= button and type the function in one of the rows. Having written the function, we can push GRAPH to draw it.
We want to find the distances for s≤ 1. This means that we will find the points that y-coordinates are smaller than or equal to 1. To do so we will determine the point that the y-coordinate is 1. To find it push 2nd, TRACE, and choose the first option, value. Then, pick a best guess for x.
From the graph we can see that the y-values are smaller than or equal to 1 for the corresponding x-values that are bigger than or equal to 40. Let's write this situation for s and d.
y ≤ 1 ⇔ x ≥ 40
s ≤ 1 ⇔ d ≥ 40
b We will find the signal strength at 10 miles, 1 mile, and 0.1 miles one at a time. To do so we will substitute these values into the given function. Let's calculate them using a table.
1600/d^2
s=1600/d^2
10 miles
1600/10^2=1600/100
16
1mile
1600/1^2=1600/1
1600
0.1 miles
1600/(0.1)^2=1600/0.01
160 000
c Notice that in the table in Part B the strength of a signal increases as the distance decreases. Therefore, while our car is getting closer to the second radio station the signal is getting stronger. It is because of this our car radio can tune into the second station.
