Question

The streptococci bacteria population N at time t (in months) is given by N = N0e 2t where N0 is the initial population. If the initial population was 100, how long does it take for the population to reach one million?

Answer 1

I’m not sure what e is in your equation. But I think the answer is t=5000 months. Let me know if you need an explanation

Answer 2

Approximately 4.61 months are needed for the streptococci bacteria population to increase from 100 to one million under exponential growth.

Step-by-step explanation:

The question is about calculating the time it takes for the streptococci bacteria population to increase from an initial population (N0) to a final population (N) under exponential growth. As given, the exponential growth formula is N = N0e2t, where 't' is the time in months.

We need to find 't' when N0=100 and N=1,000,000. Let's substitute these values into the equation: 1,000,000 = 100e2t. To simplify, divide both sides by 100 to get: 10,000 = e2t. Next, take the natural logarithm (ln) on both sides: ln(10,000) = 2t. Finally, solve for 't' by dividing by 2: t = ln(10,000)/2.

By using a calculator, we find t ≈ 4.61 months. So, it will take approximately 4.61 months for the streptococci bacteria population to increase to one million from an initial population of 100.

Learn more about Exponential growth