5) Suppose that a very contagious virus is introduced to a population. Scientists work quickly to find a vaccine to limit the number of people who will be infected. Studies show that P percent of the population will be infected t weeks after the virus is first detected according to the equation: 30 P(t) = 1+25e-0.2t a. Sketch the graph of this function. b. Estimate the time (in weeks) when the virus seems to spreading at the fast rate. c. When the virus is first detected at time t = 0, what percent of the population has the virus according to this model?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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5) Suppose that a very contagious virus is introduced to a population. Scientists work quickly to find a vaccine to limit
the number of people who will be infected. Studies show that P percent of the population will be infected t weeks after
the virus is first detected according to the equation:
30
P(t) =
1+25e-0.2t
a. Sketch the graph of this function.
b. Estimate the time (in weeks) when the virus seems to spreading at the fast rate.
c. When the virus is first detected at time t = 0, what percent of the population has the virus according to this
model?
d. Approximately how many weeks will it take for 25% of the population to be infected?
Transcribed Image Text:5) Suppose that a very contagious virus is introduced to a population. Scientists work quickly to find a vaccine to limit the number of people who will be infected. Studies show that P percent of the population will be infected t weeks after the virus is first detected according to the equation: 30 P(t) = 1+25e-0.2t a. Sketch the graph of this function. b. Estimate the time (in weeks) when the virus seems to spreading at the fast rate. c. When the virus is first detected at time t = 0, what percent of the population has the virus according to this model? d. Approximately how many weeks will it take for 25% of the population to be infected?
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