Respuesta :
Answer:
537 students
11 days
Step-by-step explanation:
5000
y= -----------------
(1+4999e^-0.8t)
a) after 8 days means t =8
5000
y= -----------------
(1+4999e^-0.8*8)
5000
y= -----------------
(1+4999e^-6.4)
5000
y= -----------------
(1+8.306)
5000
y= -----------------
(9.306)
y =537.28
Rounding to the nearest student
y = 537 students
b) 1/2 the student population means y =2500 (The 5000 is the student population)
5000
2500= -----------------
(1+4999e^-0.8t)
Multiply each side by (1+4999e^-0.8t)
2500 (1+4999e^-0.8t) = 5000
Divide each side by 2500
(1+4999e^-0.8t) = 5000/2500
(1+4999e^-0.8t) = 2
Subtract 1
(4999e^-0.8t) = 2-1
(4999e^-0.8t)=1
Divide by 4999
(4999/4999e^-0.8t)=1/4999
e^-0.8t=1/4999
Take the natural log of each side
ln(e^-0.8t)=ln(1/4999)
-.8t = ln(1/4999)
Divide by -.8
-.8/-8t = -1/.8 *ln(1/4999)
t = -1/.8 *ln(1/4999)
t≈10.6462
Rounding, it will take 11 days
We apply the use of algebraic equations and natural logarithm to solve the above question.
Natural logarithm is represented in short form as "In". It is the logarithm to the base constant of e.
The number of students affected after 8 days is 537 students
It will take 11 days for half the student population to be affected.
From the question, we are given the equation:
y= 5000/(1+4999e^-0.8t)
where
y = number of students infected after t days.
- Step 1: a) To calculate the number of students affected after 8 days, this means,
t = 8
Substituting 8 for t in the above equation,
y= 5000/(1+4999e^-0.8t)
y= 5000/(1+4999e^-0.8 x 8)
y =537.28 students
Approximately to the nearest whole number,
y = 537 students
Therefore, 537 students will be affected after 8 days.
- Step 2: b) The student population = 5000
Half the student population = 5000/2 = 2500
Hence, y = 2500
2500 = 5000 / (1+4999e^-0.8t)
Cross Multiply
2500 (1+4999e^-0.8t) = 5000
Divide both sides by 2500
(1+4999e^-0.8t) = 5000/2500
(1+4999e^-0.8t) = 2
Collect like terms
(4999e^-0.8t) = 2-1
(4999e^-0.8t) = 1
Divide both sides by 4999
(4999 / 4999e^-0.8t)=1/4999
e^-0.8t=1/4999
Take the natural logarithm of both sides
In (e^-0.8t) = In(1/4999)
-0.8t = -8.52
Divide both sides by -0.8
-0.8/-8t = -8.52/-0.8
t = 10.6462 days
Approximately to the nearest whole number
= 11 days
Therefore, it will take 11 days for half the student population to be infected.
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https://brainly.com/question/20420649
