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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Medicine On a college campus of 5000 students, the spread of a flu virus through the student body is modeled by

P = 5000 1 + 4999 e 0.8 t ,    t 0 where P is the total number of infected people and t is the time in days.

(a) Find the number of students infected after 5 days.

(b) Use a graphing utility to graph the model. Find the number of days it takes for 2000 students to become infected with the flu.

(c) According to this model, will all the students on campus become infected with the flu? Explain your reasoning.

(a)

To determine

To calculate: The number of students infected after 5 days when the college campus consists of 5000 students and the total number of people P infected by the spread of a flu virus increases with time t (in days) is given by the model as,

P=50001+4999e0.8t

Explanation

Given Information:

The college campus consists of 5000 students and the total number of people P infected by the spread of a flu virus increases with time t (in days) is given by the model as,

P=50001+4999e0.8t

Calculation:

Consider that the college campus consists of 5000 students and the total number of people P infected by the spread of a flu virus increases with time t (in days) is given by the model as,

P=50001+4999e0

(b)

To determine

To graph: The model by using technology which represents the total number of people P infected by the spread of a flu virus increases with time t (in days) is given as,

P=50001+4999e0.8t

Also determine the number of days in which the number of students infected by the flu will reach 2000.

(c)

To determine

Whether all the students of the campus would become infected or not with the flu in future and give reason when the college campus consists of 5000 students and the total number of people P infected by the spread of a flu virus increases with time t (in days) is given by the model as,

P=50001+4999e0.8t

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