Question $1$

Suppose a rumor is going around a group of $214$ people. Initially, only $40$ members of the

group have heard the rumor, but $2$ days later $65$ people have heard it$.$ Using a logistic growth

model, how many people are expected to have heard the rumor after $8$ days total have passed

since it was initially spread? $($Round your answer to the nearest whole person.$)$

Logistic Growth Model

$\frac{dP}{dt}=kP(C-P)$

where $k$ is a constant and $C$ is the carrying capacity of the population $P.$

HINT:

$\frac{1}{P(C-P)}=\frac{1}{C}(\frac{1}{P}+\frac{1}{C-P})$

Warning!

Only round your final answer according to the problem requirements. Be sure to keep

as much precision as possible and do not round during intermediate numbers.