Question

suppose that a population of yeast, satisfying geometric progression, grows 20% in an hour. if the population at the end of the first hour is 50,000 yeast, find the population at the end of 4 hours.

Answer 1

The population at the end of 4 hours is 103,680 yeast.

Step-by-step explanation:

To find the population at the end of 4 hours, we can use the formula for geometric progression:

P = P0 * (1 + r)^n

Where:
P is the final population
P0 is the initial population
r is the growth rate as a decimal
n is the number of time intervals

In this case, P0 = 50,000, r = 20% = 0.2, and n = 4.

Plugging these values into the formula:

P = 50,000 * (1 + 0.2)^4

Simplifying further:

P = 50,000 * 1.2^4

P = 50,000 * 2.0736

P = 103,680