Question

A bacteria colony increased at a rate of 4.0575e^(1.3t) bacteria per hour. If the initial polpulation is 42 bacteria, fonf thr populstion 4 hours later

Answer 1

aus! - 4.0575 e 13t popolutatis A bout eria Colony uncreased at a rate of barteria per hour. ich intial is 42 bacteria then find the population thours later Ans: het ylt) number of bacteria at timet Crven rate unerease of bacteria per hour 4.0575 e dylt) dt and untial poputation 42 bacteria 42 of ie 13t 4 .0575e 2 ie y lo) Now 1.3t dylt) 4.0575 e dt 13t dy 4.0575 e dt Integrating both sides, weget 13t dt sdy Y(t) 4.0575 e 1.3 where c is constant of integration +C /4-0575e 13t te y (t) = 4.0575 e 1.3 t Yet) = 3.121154 e 1.3t +C 13

Given 3 Y(0) = 42 Put it o it=0 and y=42 in , weget 42 = 3.121154 e 1.3.0 + c 42 -3.121154 IC 30.87 88 46 Put value of c in 6 we get 3. 121154 e + 30.078 846 we find the population 4 years later. Put A = 4 1.3344 3.121154 e 5.2 31121154 e 1.3t 4 + 38.878846 +30.878 846 y (4) = 604.6574209 No. of bacteria in A years later = 605 (Rounding off) Result: Number years later = 6050 of bacteria in A Thanking you!!