Question

Suppose a culture of 80 bacteria is put into a petri dish and the culture doubles every hour. Predict between which whole number hours the number of bacteria will be 750,000.

A) 5 to 6 hours
B) 6 to 7 hours
C) 7 to 8 hours
D) 8 to 9 hours

Answer 1

The number of bacteria will be 750,000 between 8 to 9 hours.

Step-by-step explanation:

The question is asking us to determine the time range during which a culture of bacteria, starting with 80 and doubling every hour, would reach a population of 750,000. To predict when there will be 750,000 bacteria we need to understand exponential growth.

We begin with 80 bacteria and double the amount every hour. After one hour, the population is 160, after two hours it's 320, and so on. To find out between which whole number hours the number of bacteria will be 750,000, we need to calculate the number of hours it takes for the bacteria to reach that number. Since the culture doubles every hour, we can set up an equation:

80 * 2^n = 750,000

where n is the number of hours. To solve for n, we can take the logarithm base 2 of both sides:

n = log2(750,000/80)

n is approximately 13.9. This means that after about 13.9 hours, the number of bacteria will be 750,000. Therefore, the answer is D) 8 to 9 hours.