Colby and Jaquan are growing bacteria in an experiment in a laboratory. Colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. Jaquan has a different type of bacteria that doubles every 3 hours. How many bacteria should Jaquan start with so that they have the same amount at the end of a day?

Answer 1

Let's first calculate how many bacteria Colby will have at the end of a day.

Since the number of bacteria doubles every 2 hours, after 24 hours (1 day), the number of bacteria will double 12 times:
50 * 2^12 = 50 * 4096 = 204,800 bacteria

Now, let's calculate how many bacteria Jaquan should start with so that he has the same amount at the end of a day.

Since the number of bacteria doubles every 3 hours, after 24 hours (1 day), the number of bacteria will double 8 times:
Let x be the number of bacteria Jaquan should start with.
x * 2^8 = 204,800
x = 204,800 / 256
x = 800

So, Jaquan should start with 800 bacteria in order to have the same amount as Colby at the end of a day.