Answer to Question #121586 in Algebra for ABDUL

Question

CORONA infected people in a small town grows proportional to its existing
patients. Initially the number of infected people was 50000 and the COVID-19
positive people grow at a rate of 4% per week. Formulate the suitable
mathematical model and solve the following cases by Modified Euler’s method.
a) The number of patients after 3 weeks.
b) How long it will take to double the patients.

Answer 1

CORONA infected people in a small town grows proportional to its existing patients. 

$N(t)=N(0)e^{rt}$

Given $N(0)=50000, r=0.04$

a)

$N(3)=50000e^{0.04(3)}=56475 (people)$

$N(3)=56475\ people$

b)

$N(t_1)=2N(0)$

$2N(0)=N(0)e^{rt_1}$

$e^{rt_1}=2$

$rt_1=\ln 2$

$t_1={\ln 2\over r}$

$t_1={\ln 2\over 0.04}$

$N(17)=50000e^{0.04(17)}=$

$=98694\ people<2\times50000\ people$

$N(18)=50000e^{0.04(18)}=$

$=102722\ people>2\times50000 \ people$

$t_1=18\ weeks$