(a) Are D(t) and E(t) functions or not? Explain your answer. (b) Solve fora and b if the maximum value of f(t) on the interval [0, 48] is at the point (32; 24900). (c) At what week in the interval is g(t) at its minimum?

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Chapter1: Functions
Section1.2: Functions Given By Tables
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2. Unfortunately many people have died in South Africa due to the COVID-19 pandemic.
The black graph below shows the number of people over age 1 year who have died per
week (from all possible causes, not only COVID-19) in South Africa between 29 December
2019 and 12 June 2021. We will call this black graph D(t). The solid orange graph shows
how many people are normally expected to die per week, carrying on to the end of 2021.
We will call this graph E(t). (The dotted lines are just to show that the actual values may
be a little different to E(t).)
South Africa Weekly Deaths from All Causes 1+ years: 29 Dec 2019-12 June 2021
5.00
20,000
15,000
.000
- Weekiy deatns
Lower Pedictlon Bound per Predicuon.Bound
[Downloaded from https://www.samrc.ac.za on 16.06.2021.]
The functions f(t) and g(t) have similar shapes to D(t) and E(t) respectively. They are
sketched below on the interval 0,48]. measuring t in weeks and taking t= 0 on 1 June
2020.
23
8695
+7176 + b
256
16
64
9(4)=2000 cos
30
8500
社
Transcribed Image Text:2. Unfortunately many people have died in South Africa due to the COVID-19 pandemic. The black graph below shows the number of people over age 1 year who have died per week (from all possible causes, not only COVID-19) in South Africa between 29 December 2019 and 12 June 2021. We will call this black graph D(t). The solid orange graph shows how many people are normally expected to die per week, carrying on to the end of 2021. We will call this graph E(t). (The dotted lines are just to show that the actual values may be a little different to E(t).) South Africa Weekly Deaths from All Causes 1+ years: 29 Dec 2019-12 June 2021 5.00 20,000 15,000 .000 - Weekiy deatns Lower Pedictlon Bound per Predicuon.Bound [Downloaded from https://www.samrc.ac.za on 16.06.2021.] The functions f(t) and g(t) have similar shapes to D(t) and E(t) respectively. They are sketched below on the interval 0,48]. measuring t in weeks and taking t= 0 on 1 June 2020. 23 8695 +7176 + b 256 16 64 9(4)=2000 cos 30 8500 社
(a) Are D(t) and E(t) fuctions or not? Explain your answer.
(b) Solve for a and b if the maximum value of f(t) on the interval (0, 48] is at the point
(32; 24900).
(c) At what week in the interval is g(t) at ita minimum?
(d) At what week in the interval is g(t) increasing the fastest?
(e) Calculate the integral
(/t) - g(t))dt.
(f) Explain clearly what the units are for your answer in (e) and what it represents.
(g) In a short paragraph or two explain why the integral in (e) may be the best way to
caleulate the impact of the COVID-19 pandemic on people's lives.
Transcribed Image Text:(a) Are D(t) and E(t) fuctions or not? Explain your answer. (b) Solve for a and b if the maximum value of f(t) on the interval (0, 48] is at the point (32; 24900). (c) At what week in the interval is g(t) at ita minimum? (d) At what week in the interval is g(t) increasing the fastest? (e) Calculate the integral (/t) - g(t))dt. (f) Explain clearly what the units are for your answer in (e) and what it represents. (g) In a short paragraph or two explain why the integral in (e) may be the best way to caleulate the impact of the COVID-19 pandemic on people's lives.
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