Answer:
P(t) is directly proportional to N and N'.
Where P is the increase in numbers of students who have heard the exam's cancellation rumor at any time t;
N is numbers of students who have heard the rumor of the exam's cancellation;
N' is numbers of students who have not heard the rumor of the exam's cancellation;
N' = (80 - N). Since the total number of students is 80;
K is the constant of the proportionality.
K is calculated to be 9/700
Therefore,
P(t) = KNN'
P(t) = (9/700) x N x (80 - N)
Step-by-step explanation:
The total number of students is 80. For N, N' = 80 - N.
Initially, 1 thousand people heard the rumor.
Within/after a day, the increased in number of students who have heard the rumor is P = 10 - 1 = 9
P = 9 = K x 10x (80-10)
9 = K x 10 x 70 = 700K.
Divide both sides by 700,
9/700 = (700/700)K
K = 9/700
Subtitle K into the equation P(t) = KNN'
P(t) = (9/700) x N x N'
P(t) = (9/700) x N x (80 - N), where N' = 80 - N
