Question

A bacteria has an initial population of 700 and is doubling every hour. The bacteria reaches a population of 26,000 bacteria.

a. Write an equation that could represent the situation described.

b. How long does it take for the bacteria to reach 45,000?

Please specify what you need assistance with, either part (a) or part (b), or both.

Answer 1

The exponential growth of bacteria can be represented by the equation N = N0 * 2^t, where N is the final population, N0 is the initial population, and t is the number of hours. To find the time it takes for the bacteria population to reach a certain number, we rearrange the equation and solve for t using logarithms.

Step-by-step explanation:

The situation described involves exponential growth, commonly seen in the reproduction of bacteria through prokaryotic fission. To represent the bacteria population doubling every hour, we can use the formula:

N = N0 * 2t

Where N is the final population, N0 is the initial population, and t is the number of hours. For part (a), the initial population is 700, so:

26000 = 700 * 2t

For part (b), to find the time (t) it takes for the bacteria to reach a population of 45,000, we set up the equation:

45000 = 700 * 2t

Then solve for t using logarithms:

t = log2(45000/700) = log264.2857 ≈ 6 hours

It takes approximately 6 hours for the bacteria population to reach 45,000.