Pre Cal Math Help!!!

Question

A bacteria culture contains 1300 bacteria initially and doubles every hour.

(a) Find a function that models the number of bacteria n(t) after t hours.
n(t) =

(b) Find the number of bacteria after 24 hours.
bacteria

Answer 1

MADZ, this is an exponential growth problem in which it can be modeled a number of ways. For simplicity, lets use this model.

 

(a) n(t)=n_o*2^t  where n_o = the initial amount of bacteria at time equals to zero.

                                 t = the time in hours

 

Hence, n(t)=1300*2^t

 

(b)  n(24)=1300*2²⁴=2.181038*10¹⁰

 

Note: Many problems involving exponential growth is modeled as n(t)=n_o*e^kt .