Question

The spread of CORONA virus is given by the equation,

Q=Q.e^rt

If there were initially 500 people infected by the virus by March 2020 and t is given in weeks, and r is the growth rate of the virus.

I. How many people are infected after 84 days when the growth rate is 0.195? [4 Marks]

II. At what rate will cause the infected number of people to rise to 1500 in 21 days? [5 Marks]

III. How long will it take for the initial number of infected to be quadrupled if the growth rate was at 0.21? [6 Marks]

Answer 1

1.) Given that lo=500 people p=0.195 t= bu days t = 84 = 12 weeks @= q ert Q = 500 e0195412 Q = 500x (2-7110.195x12 Q = soo x 2.70)2:34 @=5153.68 u Sis 3 people Thus, infected people will reach 5133 after 12 weeks. let growth rate=8 Q = 1500, o = 500 Q = Bert a = ert lng = lnert 0.693 logg = rt 0.693 log 1600 = r x 2

0.693 1098=38 r = 0.693 x 1093 r= 0.1102 Thus, growth rate will be 0.1102 when infected people will become 1500 in 21 days. Civen that, initial people quadruples il . Q = UQ. ,8 = 0.21 Using equation from previous part, Ing =Y 0.693 log(400) = 0.217 0.693 logu = 0.21t te 0.693x2x1092 u 1696 weeks 0.21 & 2 weeks t = 1.98 weeks = 1.98*7 = 13.90 daus. u Mdays Thus it will take around 14 days so that number of infected people quadruples at growth rate of 0:21.