Question

In a city, a rumour is spreading about the safety of corona vaccination. Suppose NN number of people live in the city and f(t)f(t) is the number of people who have not yet heard about the rumour after tt days. Suppose f(t)f(t) is given by f(t)=Ne−ktf(t)=Ne−kt, where kk is a constant. If the population of the city is 10001000, and suppose 4040 have heard the rumor after the first day. After how many days (approximately) half of the population would have heard the rumor?​

Answer 1

Given : $f(t)=Ne^{-kt}$

N = number of people live in the city

f(t) = the number of people who have not yet heard about the rumour after t

k is a constant

the population of the city is 1000

40 have heard the rumor after the first day.

To Find :  After how many days (approximately) half of the population would have heard the rumor ​

Solution:

$f(t)=Ne^{-kt}$

people not heard after 1 day  = 1000 - 40  = 960

t = 1

=>  $960=1000e^{-k\cdot 1}$

=> k = 0.0408

half of the population would have heard the rumor ​ = 500

Not heard = 500

$500=1000e^{-k\cdot t}$

=> ln 2 =  kt

=> 0.69315  = ( 0.0408) t

=> t = 16.98

Hence after 17 Days

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