Question

The population of bacteria in a petri dish is increasing exponentially. At noon, there were 32,600 bacteria in the dish. An hour later, there were 34,556 bacteria. Write a function to model this situation. Determine the percent increase of the bacteria each hour.

Answer 1

To model this situation, we can use the exponential growth equation:

N(t) = N0 * e^(rt)

where N(t) is the population at time t, N0 is the initial population, e is the base of the natural logarithm (approximately equal to 2.718), r is the growth rate, and t is the time elapsed.

We can use the given information to solve for r:

34,556 = 32,600 * e^(r*1)

e^(r*1) = 34,556 / 32,600

e^(r*1) = 1.0604

r = ln(1.0604)

r ≈ 0.0599

So the function that models the population of bacteria in the petri dish is:

N(t) = 32,600 * e^(0.0599t)

To determine the percent increase of the bacteria each hour, we can use the formula:

percent increase = [(new population - old population) / old population] * 100%

For the first hour, the old population is 32,600 and the new population is 34,556, so:

percent increase = [(34,556 - 32,600) / 32,600] * 100%

percent increase ≈ 5.98%

Therefore, the bacteria population is increasing by approximately 5.98% each hour.