Question

3. Growth of Cholera bacteria. Suppose that the cholera bacteria in a colony grows unchecked according to the Law of Exponential Change. The colony starts with 1 bacterium and doubles in number every half hour. a. How many bacteria will the colony contain at the end of 24 h

Answer 1

2.814 * 10^14

Explanation:

For exponential growth:

A = A0*e^kt

A = final amount ; A0 = initial amount ; t = time

Since bacterium doubles ever half hour ;

In 1 hour number of bacterium will be 2² = 4

Hence

Final amount after 1 hour

4 = 1*e^k*1

4 =e^k

Take In of both sides

In(4) = k

Number of bacterium in 24 hours

A = 1*e^In4 * 24

A = e^24In4

A = e^33.271064

A = 281474976710656

A = 2.814 * 10^14