Final answer:
It will take approximately 54 hours for the population of bacteria to grow from 500 to 800, when doubling every 24 hours, as this is an example of exponential growth.
Step-by-step explanation:
To determine how long it will take for the population of bacteria to reach 800 from an initial population of 500, given that it doubles every 24 hours (exponential growth), we can use the formula for exponential growth: N = N0 × 2^(t/T), where N is the final population size, N0 is the initial population size, t is the time in hours, and T is the doubling time in hours. We want to find the time t when N = 800 and N0 = 500. We can solve this by rearranging the formula to solve for t:
t = T × (log(N/N0) / log(2))
Substituting in the known values, we get:
t = 24 × (log(800/500) / log(2))
Using a calculator, we get:
t = 24 × (log(1.6) / log(2))
t = 24 × (0.6781 / 0.3010)
t ≈ 54.0 hours
So it will take approximately 54 hours for the population to grow from 500 to 800 bacteria. This example demonstrates how the population growth rate is accelerating, a key characteristic of exponential growth.