Question

Eric is culturing bacteria that have a growth rate of 5% per hour. If the current population is 76,683 bacteria, how many bacteria will there be in 12 hours? If necessary, round your answer to the nearest whole number.

Answer 1

To determine the number of bacteria in 12 hours, use the exponential growth formula N = P * (1 + r)^t, where N is the final population, P is the initial population, r is the growth rate, and t is the time. Plugging in the values gives approximately 151,327 bacteria.

Step-by-step explanation:

To determine the number of bacteria in 12 hours, we need to use the exponential growth formula. The formula is given by:

N = P * (1 + r)^t

Where:

• N is the final population
• P is the initial population
• r is the growth rate (expressed as a decimal)
• t is the time in hours

In this case, the initial population (P) is 76,683, the growth rate (r) is 0.05 (or 5% expressed as a decimal), and the time (t) is 12 hours. Plugging these values into the formula gives:

N = 76,683 * (1 + 0.05)^12

Calculating the result gives approximately 151,327 bacteria. Therefore, there will be around 151,327 bacteria after 12 hours.