Question

Under ideal conditions a certain bacteria population is known to double every 2 hours. Suppose there are initially 500 bacteria. 1. What is the size of the population after 6 hours? Answer: 2. What is the size of the population after t hours? Answer: 3. Estimate the size of the population after 19 hours. Answer:

Answer 1

A)4000bacteria b) 500*2^(t/2) c) 362039 bacteria

Step-by-step explanation:

The bacteria population doubles every 2hrs.

Initial population = 500 bacteria

After 6hours, it will undergo 3 generations since

6hours /2hrs = 3.

That means it has doubled its population three times

Initial is 500

After 2hrs = 1000bacteria, 4hrs = 2000 bacteria,

6hrs = 4000 bacteria

B) after 2hrs, the population is 500*2^1,

After 4hrs, the population is 500* 2^2,

After 6hrs, the population is 500*2^3

Which is the same as 500*2^(6/2)

Then after t hours, the population is 500*2^(t/2)

C) after 19 hours, the populations = 500*2^(19/2)

= 362038.67 approx 362039 bacteria