Answer:
On the 12th day, the rumor would have has to all the 1000 employees
Step-by-step explanation:
Given the data in the question;
so, lets consider the rumor spreading thorough the company of 1000 employee;
the given model is; =
+ 1000k
( 1000 -
)
where k is the parameter that depends on how fast the rumor spreads, n is the number of days.
now, lets assume k = 0.0001, lets also assume r₀ = 4
so to find how soon all 1000 employees will have heard the rumor ;
let n be;
then r1 will be;
r1 = r₀ + ( 0.001)r₀(1000-r₀ )
so
r1 = 4 + ( 0.001) × 4× (1000 - 4 )
r1 = 7.984
r2 will be;
r2 = r1 + ( 0.001)r1(1000-r1 )
r2 = 7.984 + ( 0.001) × 7.984 × (1000 - 7.984 )
r2 = 15.904255744
r3 will be;
r3 = r2 + ( 0.001)r2(1000-r2 )
r3 = 15.904255744 + ( 0.001) × 15.904255744 × (1000 - 15.904255744 )
r3 = 31.555566137
Using the same formula and procedure by substituting n = 1,2,3,4,5,6,7,8,9,10,11,12.
we will have;
n rₙ
0 4
1 7.984
2 15.904255744
3 31.555566137
4 62.1153785
5 120.372437
6 226.25535
7 401.319217
8 641.58132
9 871.53605
10 983.497013
11 999.727651
12 999.999926
Therefore, On the 12th day, the rumor would have has to all the 1000 employees