Question

Biologists are studying a new bacterium. They create a culture with 100 of the bacteria and anticipate that the number of bacteria will double every 30 hours. Write an equation for the number of bacteria, B, in terms of the number of hours, t, since the experiment began.

A) B = 100(2^(t/30))
B) B = 100(2t/30)
C) B = 100(2t)
D) B = 100(t/30)

Answer 1

The equation representing the number of bacteria in the culture, which doubles every 30 hours, starting with 100 bacteria, is B = 100(2^(t/30)).

Step-by-step explanation:

The number of bacteria in the culture is an example of exponential growth, which occurs when the growth rate increases at a constant percentage per time unit. As the question states, the bacteria double every 30 hours, and the starting number is 100. To model this growth, you would use the formula for exponential growth:

B = 100(2(t/30))

This equation represents the number of bacteria, B, after a certain number of hours, t. If you want to find the number of bacteria at any time, simply plug in the value of 't' into the equation and calculate B. This formula accurately depicts the doubling nature of the bacteria's growth over time.