Calculus question

Question

A population of bacteria, growing exponentially, quadruples its number in four hours. How long does it take for the number of bacteria to be 1.5 times of the original number?

Answer 1

Let A₀ be the initial population

 

A(t) = A₀e^kt = population in t hours

 

A(4) = A₀e^4k = 4A₀

 

So, e^4k = 4

 

     ln(e^4k) = ln4      4k = ln4

 

                               k = 0.3466

 

Therefore, A(t) = A₀e^0.3466t

 

Find t so that A(t) = 1.5A₀ :  1.5A₀ = A₀e^0.3466t

 

                                             1.5 = e^0.3466t

 

                                           ln1.5 = 0.3466t

 

                                              t = 1.17 hours ≈ 1 hr 10 min