Given the function:
[tex]y=\frac{3600}{1+899e^{-0.6x}}[/tex]Let's solve for the following:
(a) Graph the function for 0≤x≤15.
This is an exponential function.
This graph will stop increasing at y = 3600
Thus, we have the graph below:
The graph that correctly represents this situation is graph C.
(b) How many students had the virus when it was first​ discovered?
Here, we are to find the y-intercept.
At the y-intercept, the value of x is zero.
Now, substitute 0 for x and solve for y:
[tex]\begin{gathered} y=\frac{3600}{1+899e^{-0.6x}} \\ \\ y=\frac{3600}{1+899e^{-0.6(0)}} \\ \\ y=\frac{3600}{1+899e^0} \\ \\ y=\frac{3600}{1+899} \\ \\ y=\frac{3600}{900} \\ \\ y=4 \end{gathered}[/tex]Therefore, the number of students that had the virus when it was first discovered is 4.
(c) What is the upper limit of the number infected by the virus during this​ period?
Here, we have the limit 0≤x≤15.
This means the upper limit infected during this period will be at x = 15 .
Substitute 15 for x and solve:
[tex]\begin{gathered} y=\frac{3600}{1+899e^{-0.6(15)}} \\ \\ y=\frac{3600^{}}{1+899(0.0001234)} \\ \\ y=3240.48 \end{gathered}[/tex]Therefore, the upper limit of the number infected by this virus in [0, 15] is 3240.48
ANSWER:
(b) 4 students
(c) 3240.48
