Question

Suppose y(t)40e^2t+8 represents the number of the bacteria present at time t minutes. At what time will the population reach 100 bacteria?(note : answers are expressed in terms of the natural logarithm.)

Answer 1

t = ln (2.3) / 2

Step-by-step explanation:

y(t) = 40 e^2t + 8

Let y(t) = total population within a time frame

According to the question, y(t) = 100

100 = 40 e^2t + 8

Collect the like terms

100 - 8 = 40 e^2t

92 = 40 e^2t

Divide both sides by 40

92/40 = 40 e^2t / 40

2.3 = e^2t

Take the natural logarithms of both sides

ln (2.3) = ln (e^2t)

ln (2.3) = 2t

Divide both sides by 2

ln (2.3) / 2 = 2t / 2

t = In (2.3) / 2 in terms of the natural logarithms

t = 0.8329 / 2

t = 0.4 mins