An experimental culture has an initial population of 50 bacteria.The population increased by 80 percent in 20 minutes.Determine the time it will it take to have a population of 1.2 million bacteria?

Answer 1

To determine the time it will take to reach a population of 1.2 million bacteria, we need to find the growth rate per minute and then calculate the time it will take for the population to reach 1.2 million.

The population increased by 80 percent in 20 minutes, so the growth rate per minute can be calculated as:
Growth rate per minute = 80% / 20 minutes = 4% per minute

Let's denote the time it will take for the population to reach 1.2 million bacteria as t minutes.

Using exponential growth formula: Final population = Initial population * (1 + growth rate)^time, we can write:
1.2 million = 50 * (1 + 0.04)^t

Divide both sides of the equation by 50:
24,000 = (1.04)^t

To isolate the exponent, take the logarithm (base 1.04) of both sides:
log base 1.04 (24,000) = log base 1.04 ((1.04)^t)

Simplify the equation:
t = log base 1.04 (24,000)

Using a calculator, we find that log base 1.04 (24,000) ≈ 289.1

Therefore, it will take approximately 289.1 minutes for the population to reach 1.2 million bacteria.