There have been many reports in the media about "flattening the curve" showing pictures like the one below. The x-axis measures time t in days, and the y-axis measures the number of people contracting the Covid-19 illness per day. A function that has this sort of shape is k 9(t) = g(t): where k is a fixed constant. %3D k + t2 (a) Sketch the graph of g(t) for k = 3. Show all your working and clearly indicate any asymptotes, intervals on which the function is increasing or decreasing, maxima or minima, intervals of concavity and points of inflection. (b) The graph of g is symmetric about the y-axis. Find the value of k so that its points of inflection are at t = -10 and t = 10. (c) Using the value of k you found in (b) alter the formula of g(t) by scaling and shifting to get a new function with maximum point at (60; 400) and points of inflection at t = 50 and t = 70. Call this function h(t), write down its formula and draw a rough sketch showing the shape of h(t). r60 (d) Explain in words what the definite integral h(t) dt calculates and indicate this on your graph in (c). (You do not need to calculate the integral.) (e) Your friend looks at the graph of h(t) and says that at t = 65 it is good because there are fewer people who are ill with Covid-19. Do vou agree or disagree? Explain.
There have been many reports in the media about "flattening the curve" showing pictures like the one below. The x-axis measures time t in days, and the y-axis measures the number of people contracting the Covid-19 illness per day. A function that has this sort of shape is k 9(t) = g(t): where k is a fixed constant. %3D k + t2 (a) Sketch the graph of g(t) for k = 3. Show all your working and clearly indicate any asymptotes, intervals on which the function is increasing or decreasing, maxima or minima, intervals of concavity and points of inflection. (b) The graph of g is symmetric about the y-axis. Find the value of k so that its points of inflection are at t = -10 and t = 10. (c) Using the value of k you found in (b) alter the formula of g(t) by scaling and shifting to get a new function with maximum point at (60; 400) and points of inflection at t = 50 and t = 70. Call this function h(t), write down its formula and draw a rough sketch showing the shape of h(t). r60 (d) Explain in words what the definite integral h(t) dt calculates and indicate this on your graph in (c). (You do not need to calculate the integral.) (e) Your friend looks at the graph of h(t) and says that at t = 65 it is good because there are fewer people who are ill with Covid-19. Do vou agree or disagree? Explain.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 47E
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Transcribed Image Text:There have been many reports in the media about "flattening the curve" showing pictures
like the one below. The x-axis measures time t in days, and the y-axis measures the
number of people contracting the Covid-19 illness per day.
A function that has this sort of shape is
k
9(t) =
g(t):
where k is a fixed constant.
%3D
k + t2
(a) Sketch the graph of g(t) for k = 3. Show all your working and clearly indicate any
asymptotes, intervals on which the function is increasing or decreasing, maxima or
minima, intervals of concavity and points of inflection.
(b) The graph of g is symmetric about the y-axis. Find the value of k so that its points
of inflection are at t = -10 and t = 10.
(c) Using the value of k you found in (b) alter the formula of g(t) by scaling and shifting
to get a new function with maximum point at (60; 400) and points of inflection at
t = 50 and t = 70. Call this function h(t), write down its formula and draw a rough
sketch showing the shape of h(t).
r60
(d) Explain in words what the definite integral h(t) dt calculates and indicate this
on your graph in (c). (You do not need to calculate the integral.)
(e) Your friend looks at the graph of h(t) and says that at t = 65 it is good because there
are fewer people who are ill with Covid-19. Do vou agree or disagree? Explain.
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