the spread of a highly contagious virus in a high school can be described by the logistic function y = 5600…

the spread of a highly contagious virus in a high school can be described by the logistic function y = 5600 / (1 + 699e^(-0.8x)) where x is the number of days after the virus is identified in the school and y is the total number of people who are infected by the virus. (a) graph the function for 0 ≤ x ≤ 15. (b) how many students had the virus when it was first discovered? (c) what is the upper limit of the number infected by the virus during this period? 0,15 by 0,5600, xscl = 2, yscl = 1000 (b) the number of students who had the virus when it was first discovered is .

the spread of a highly contagious virus in a high school can be described by the logistic function y = 5600 / (1 + 699e^(-0.8x)) where x is the number of days after the virus is identified in the school and y is the total number of people who are infected by the virus. (a) graph the function for 0 ≤ x ≤ 15. (b) how many students had the virus when it was first discovered? (c) what is the upper limit of the number infected by the virus during this period? 0,15 by 0,5600, xscl = 2, yscl = 1000 (b) the number of students who had the virus when it was first discovered is .

Answer

Explanation:

Step1: Find initial - infected number

When the virus was first discovered, (x = 0). Substitute (x = 0) into the logistic function (y=\frac{5600}{1 + 699e^{-0.8x}}). When (x = 0), (e^{-0.8x}=e^{0}=1). Then (y=\frac{5600}{1 + 699\times1}).

Step2: Calculate the value of (y)

(y=\frac{5600}{1 + 699}=\frac{5600}{700}=8).

Step3: Find the upper - limit

For a logistic function of the form (y=\frac{L}{1 + ae^{-bx}}), the upper - limit (carrying capacity) is (L). In the given function (y=\frac{5600}{1 + 699e^{-0.8x}}), (L = 5600).

Answer:

(b) 8 (c) 5600

For part (a), graphing the function (y=\frac{5600}{1 + 699e^{-0.8x}}) for (0\leq x\leq15) can be done using a graphing utility (such as a graphing calculator or software like Desmos). Enter the function and set the (x) - range from (0) to (15) and the (y) - range from (0) to (5600) with appropriate scales ((Xscl = 2) and (Yscl=1000)).