Question

A virus jumps from monkeys to humans. The number of people P(t) who have been infected with the virus t weeks after the jump grows logistically. Suppose that initially 10 people are infected with the virus and that the continuous growth rate is 1.78. It is estimated that in the long run approximately 5000 people will have been infected with the virus. The virus is spreading the fastest approximately:________
a. 3.5 weeks after the jump.
b. 4.0 weeks after the jump.
c. 4.5 weeks after the jump.
d. 5.0 weeks after the jump.
e. None of the above is correct.

Answer 1

Answer:

e. None of the above is correct.

Step-by-step explanation:

The general formula for exponential growth is;

P= a(1 + r)^t

Where;

P = total number infected after a given time interval

a = initial number of infected people

r = growth rate of infection

x= time taken in weeks

Hence;

5000= 10(1 + 1.78)^t

5000/10 = (1 + 1.78)^t

500 = (1 + 1.78)^t

log 500 = tlog(1 + 1.78)

t = log 500/log(1 + 1.78)

t = 2.699/0.444

t = 6 weeks