0.1 Basic Exponential Growth Suppose during a recent epidemic, the number of cases of people infected with the Ebola virus grew at a rate proportional to the total number of cases. A differential equation to represent the situation described above is dN = kN dt Where N is the number of cases of Ebola, t is the time in months, and k is a constant. (a) If in March 2014, there were 50 cases and after three months, the number of cases had grown to 550. Find the value of k in the differential equation. Show all of your work. (b) Solve the differential equation from above and use the given data to find an expression for the total number of Ebola cases, N(t). Show your work. (c) How many cases of Ebola does your model predict after 10 months? Show all of your work. (d) The actual number of recorded cases after 10 months was approximately 21, 300. What do you think might be some reasons that the results of the model and those of the actual data are different?
0.1 Basic Exponential Growth Suppose during a recent epidemic, the number of cases of people infected with the Ebola virus grew at a rate proportional to the total number of cases. A differential equation to represent the situation described above is dN = kN dt Where N is the number of cases of Ebola, t is the time in months, and k is a constant. (a) If in March 2014, there were 50 cases and after three months, the number of cases had grown to 550. Find the value of k in the differential equation. Show all of your work. (b) Solve the differential equation from above and use the given data to find an expression for the total number of Ebola cases, N(t). Show your work. (c) How many cases of Ebola does your model predict after 10 months? Show all of your work. (d) The actual number of recorded cases after 10 months was approximately 21, 300. What do you think might be some reasons that the results of the model and those of the actual data are different?
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Transcribed Image Text:0.1
Basic Exponential Growth
Suppose during a recent epidemic, the number of cases of people infected with the Ebola
virus grew at a rate proportional to the total number of cases. A differential equation to
represent the situation described above is
dN
= kN
dt
Where N is the number of cases of Ebola, t is the time in months, and k is a constant.
(a) If in March 2014, there were 50 cases and after three months, the number of cases
had grown to 550. Find the value of k in the differential equation. Show all of your work.
(b) Solve the differential equation from above and use the given data to find an expression
for the total number of Ebola cases, N(t). Show your work.
(c) How many cases of Ebola does your model predict after 10 months? Show all of your
work.
(d) The actual number of recorded cases after 10 months was approximately 21, 300. What
do you think might be some reasons that the results of the model and those of the actual
data are different?
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