3. One of the ways society is trying to bring the pandemic under control is by vaccinating people against the virus. The graph below shows the number of people vaccinatedl in South Africa per day from the end of April to early in June. It is clear that the number of people being vaccinated per day has increased significantly over the past two months.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.2: Representing Data
Problem 22PFA
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Sub question iv and also b and c

3. One of the ways society is trying to bring the pandemic under control is by vaccinating
people against the virus. The graph below shows the number of people vaccinated in South
Africa per day from the end of April to early in June. It is clear that the number of people
being vaccinated per day has increased significantly over the past two months.
Jur
(Downloaded from https://www.statista.com/statistics/1231031/daily-number-of-covid-19-
vaccination-doses-in-south-africa/ on 16.06.2021.]
On 1 May 2021, 3,000 people were vaccinated and on 31 May 2021, 45,000 people were
vaccinated.
(a) Setting t = 0 on 1 May and t= 30 on 31 May, you want to find a function whose
graph looks similar to the shape above and has the same values of 3,000 at t= 0 and
45,000 at t = 30. In each of (i) to (iv) below solve for the constants a and b so that
the given function goes through the above points at t= 0 and t= 30.
i. f(t) = at² + b
ii. g(t) = ae
iii. A(t) = a + becos (t)
iv. j(t)
1+ be-1/10
(b) For each of the four functions from (i) to (iv) in (a) caleulate the value of the derivative
when t = 30. (Use the values for a and b that you calculated in (a).)
(c) Based on your answers in (b), if you were the new Minister of Health, which function
would you like to see as the function describing the number of people vaccinated per
day? Explain.
021
30, 2021
May 4, 2021
May 8, 2021
May 12, 2021
May 16, 2021
May 20, 2021
May 24, 2021
May 28, 2021
Jun 1, 2021
Jun 5, 2021
Jun 9.
Transcribed Image Text:3. One of the ways society is trying to bring the pandemic under control is by vaccinating people against the virus. The graph below shows the number of people vaccinated in South Africa per day from the end of April to early in June. It is clear that the number of people being vaccinated per day has increased significantly over the past two months. Jur (Downloaded from https://www.statista.com/statistics/1231031/daily-number-of-covid-19- vaccination-doses-in-south-africa/ on 16.06.2021.] On 1 May 2021, 3,000 people were vaccinated and on 31 May 2021, 45,000 people were vaccinated. (a) Setting t = 0 on 1 May and t= 30 on 31 May, you want to find a function whose graph looks similar to the shape above and has the same values of 3,000 at t= 0 and 45,000 at t = 30. In each of (i) to (iv) below solve for the constants a and b so that the given function goes through the above points at t= 0 and t= 30. i. f(t) = at² + b ii. g(t) = ae iii. A(t) = a + becos (t) iv. j(t) 1+ be-1/10 (b) For each of the four functions from (i) to (iv) in (a) caleulate the value of the derivative when t = 30. (Use the values for a and b that you calculated in (a).) (c) Based on your answers in (b), if you were the new Minister of Health, which function would you like to see as the function describing the number of people vaccinated per day? Explain. 021 30, 2021 May 4, 2021 May 8, 2021 May 12, 2021 May 16, 2021 May 20, 2021 May 24, 2021 May 28, 2021 Jun 1, 2021 Jun 5, 2021 Jun 9.
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