Constants A and K are
A = 18 and K = 0.014
At 10:30 am 63 people know the rumour
The rumour should have gone round the school by 2 pm
How to find the constants
From the problem we can deduce that
The starting value A = 18
To find the number of people who know the rumor at 10:30 we solve as follows
we solve for K, using the given values
42 = 18e^(60k) from 9 am to 10 am = 60 minutes
e^(60k) = 42/18
take In of both sides
60k = In(42/18)
k = 0.014
From 9 am to 10:30 am is 90 minutes
N = 18e^(90 * 0.014)
N = 63.46 = 63
To find the time when everyone in the school (1200 people) knows the rumour
1200 = 18e^(0.014 * t)
e^(0.014 * t) = 1200/18
take In of both sides
0.014t = In(1200/18)
t = 299.98 approximately 300 minutes
300/60 = 5 hours
9 am + 5 hours = 2 pm