d Where and when is the lowest point on the graph?
E
e What was the starting and finishing attendance?
A
a See solution.
B
b A(13)≈425, see solution.
C
c A(1)=400 and A(10)=400, see solution.
D
d 350 students in week 4.
E
e See solution.
Practice makes perfect
a Let's look at the given graph.
After the flu outbreak attendance quickly dropped by about 100 students over a period of four weeks. Then, over a period of 14 weeks it slowly rises back to the starting value.
b A(13) is the function notation representing the attendance numbers in week 13. Let's find the value of A(13) in the graph.
We can see that A(13) is approximately 425. This means that in week 13, the number of students in attendance was 425.
c To know which values of x make A(x)=400, we will draw a horizontal line at 400 and look where it intersects the graph of the function. Let's do it!
We can see that A(x) is approximately 400 when x= 1 and x= 10. The first value, A( 1)=400, tells us that one week after the flu outbreak attendance had dropped to 400. The second occurrence, A( 10) means that ten weeks after the outbreak, attendance had risen back to 400.
d Let's look for the value of x that makes A(x) the lowest.
The lowest attendance — when the graph is at its lowest y-value — was around 350 students and occurred around week 4.
e While there is no way to answer this question with certainty, we can make an educated guess based on the pre-flu attendance numbers. Our best guess is that approximately 450 students are enrolled in this school because that was the attendance before the outbreak.
It is also the approximate value that the graph reached 18 weeks after the outbreak.
