Question

8 boxes are usually made of this material. The number of bacteria in a petri dish can be modeled by une equation p = 2(2)n where p is the number of bacteria after n hours. a. after how many hours will there be 65,536 bacteria

Answer 1

The number of bacteria can be modeled by the equation p = 2(2)n, and we need to solve for n to find the number of hours it takes for there to be 65,536 bacteria. By simplifying the equation and taking the logarithm base 2, we find that it takes approximately 15 hours.

Step-by-step explanation:

The number of bacteria in a petri dish can be modeled by the equation p = 2(2)n, where p is the number of bacteria after n hours. To find the number of hours it takes for there to be 65,536 bacteria, we need to solve the equation for n:

65,536 = 2(2)n

First, we can simplify the equation by dividing both sides by 2:

32,768 = (2)n

Next, we can take the logarithm base 2 of both sides to solve for n:

n = log2(32,768)

Using a calculator, we find that n is approximately 15. Therefore, it will take approximately 15 hours for there to be 65,536 bacteria.

Learn more about Exponential growth