Problema Solution
The relative growth rate of a certain bacteria colony is 26%. Suppose there are 6 bacteria initially.
a)Find a function that describes the population of bacteria after t hours.
b) How many bacteria should be expected after 2 days?
a) P(t)=
Answer provided by our tutors
given , initial no. of bacteria = 6
rate of colony = 26
lets first observe some terms of the situation ......
at hr = 0
no. of bacteria = 6 = 6(1.26)0
at hr = 1
no. of bacteria = 6+ 26%of 6 = 6+0.26(6) =6(1.26)1
at hr = 2
no. of bacteria = 6(1.26) + 0.26(6(1.26)) = 6(1.26)(1.26) = 6(1.26)2
at hr = 3
no. of bacteria = 6(1.26)2+0.26(6(1.26)2)) = 6(1.26)2(1.26) = 6(1.26)3
a) therefore we can write that,
after 't' hrs i.e at hr=t
population,P(t) = 6(1.26)t which is the required function
b) after 2 days = 48 hrs
P(48)=6(1.26)48 = 6(65733.41) = 394400 (approx) => population of bacterias after 2 days
C) P(t) = 6(1.26)t