Question

An E.Coli strain has a half life (To) of 2 days in organic topsoil. If the population entering the soil is 1 million cells per litre, how long does it take to become technically terminated (< 1 unit per life)?

HINT: Rework the expression: N/N0 = (0.5)⁽ᵀ/ᵀᵒ⁾

Answer 1

To calculate how long it takes for an E. coli population to decline to less than 1 unit per liter in organic topsoil, apply the provided decay formula with a given half-life of 2 days and an initial population of 1 million cells per liter.

Step-by-step explanation:

The student's question pertains to the exponential decay of a population of E. coli bacteria in organic topsoil and how long it would take for the population to decrease to less than 1 unit per liter from an initial population of 1 million cells per liter.

This can be examined mathematically using the concept of half-life and the provided decay formula N/N0 = (0.5)⁵⃗/⁴o, where N is the final population size, N0 is the initial population size, T is the total time elapsed, and To is the half-life of the bacteria.

To solve for the time it would take for the initial population to technically terminate, we need to set N to be less than 1 unit and solve for T. Using the half-life of 2 days, we find that it will take a series of half-lives until the population reaches less than 1. Since N/N0 can be rewritten as (1/2)⁵⃗/⁴o, we can calculate the number of half-lives required to reach a population size of < 1 by solving (1/2)⁵⃗ < 1/N0, where N0 is 1 million. After finding the number of half-lives required, we can multiply by To (2 days) to get the total time elapsed.