Limits And Derivatives

Let y denote the number of bacteria at any instant t . then according to the question ......(i) k is the constant of proportionality, taken to be + ve on integrating (i), we get ....(ii) c is a parameter. let be the initial number of bacteria i.e., at using this in (ii), .....(iii) So, from (iii) , we get .........(iv) Using (iv) in (iii) let the number of bacteria become to in hours. i.e., when hours. from (v) Hence, the reqd. no. of hours