A model for the number of bacteria in a culture after t hours is given by P(t)=P_0e^(kt). After 3 hours it is observed that 400 bacteria are present. After 10 hours of 2000 are present. What is the initial number of bacteria? .... the answer in the back of the book is 201.. but i dont know how to get there. please show work!! thanks !!!!

Question

anonymous · Answer

@phi

phi · Answer

The  first step is fill in the numbers to get two equations with two unknowns
P(t)=P_0e^(kt)

 3 hours it is observed that 400 bacteria -->  400= P_0e^(k*3)
10 hours of 2000 are present -->  2000= P_0e^(10k)

to solve:  1) divide one equation by the other and solve for k
2) after you find k, use one of the equations to solve for P_0