Question

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?

Answer 1

Answer: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

Explanation: