Exponential growth
In a certain biology experiment rate of increase of number of bacterias at time t is found to be numaricaly equal to number of bacterias prasent at that time,if
a
denotes the number of bacterias prasent initialy and
b
denotes number of bacterias prasent after time
t
(in seconds) then find out the ratio of
b
and
a
after 10s
Now suppose your answer is n then find out the value of ⌊n⌋
The answer is 22026.
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1 solution
Accourding to question:- d t d b = b Rarranging:- b d b = d t Integrating both sides:- l n ( b ) = t + k . . . . . . . . . ( 1 ) Where k is constent of integration:- Now accourding to question when t=0 then b=a Putting the values in equation (1):- k = l n ( a ) Putting the value of k in equation (1):- l n ( b ) = l n ( a ) + t Rearranging and applying genral rules of log function:- l n ( a b ) = t Taking antylog both sides:- a b = e t So ratio of b and a is exponential function of time so after 10seconds:- a b = e 1 0 = 2 2 0 2 6 . 4 6 5 And its greatest integer value =22026 2 2 0 2 6