The count in a bacteria culture was 800 after 15 minutes and 1200 after 40 minutes. Assuming the count grows exponentially, What was the initial size of the culture?

1) bacteria size = b(initial) * e^(r * t)  

initial size = 300  

final size = 1600.

Substituting the values into the main equation:

1600 = 300 * e^(r * 35 - 20)  

solving for 'r'.

1600 = 300 * e^(r * 15)  

1600/300 = e^(r * 15)  

taking natural log on both sides to eliminate the power

ln(16/3) = ln[e^(r * 15)]  

ln(16/3) = r * 15  

r  = ln(16/3) / 15

  = 0.11159843

  = 11.16%  

To find the initial bacteria size,  

Given: t = 20  

300 = b * e^(0.1116 * 20)  

Solving for b:

300 = b * e^2.232  

b = 300/e^2.232  

b = 32

Step-by-step explanation:

a: 1/6, j: 1/4

step-by-step explanation: you are welcome