If y is the death toll, we note that y only starts to change after 16 January 2020. So we set t = 0 on 16 January and read the following data from the graph. t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 y 1 2 3 4 4 6 17 25 41 55 56 82 106 133 170 213 (a) Assuming that y = at, use the point (15; 213) on the graph to calculate the base a. (b) We prefer to write an exponential function y = at as y = ekt. Find the constant k given your answer for a in (a). (c) Sketch the graph of y = ekt for the value that you found for k above, for 0 t 15. Indicate a few points on the graph.
If y is the death toll, we note that y only starts to change after 16 January 2020. So we
set t = 0 on 16 January and read the following data from the graph.
t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
y 1 2 3 4 4 6 17 25 41 55 56 82 106 133 170 213
(a) Assuming that y = at, use the point (15; 213) on the graph to calculate the base a.
(b) We prefer to write an exponential function y = at as y = ekt. Find the constant k
given your answer for a in (a).
(c) Sketch the graph of y = ekt for the value that you found for k above, for 0 t 15.
Indicate a few points on the graph. (The graph you sketch will not be exactly the
same as the graph above, but is should be quite similar in shape and range.)
(d) Using your formula y = ekt, what would your function give as the death toll by 10
February 2020? What would it give as the death toll by 31 May 2020?
(e) Are the values you got in (d) realistic or unrealistic? Explain why this may be.
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