Question

If there are initially 3000 bacteria in a culture, and the number of bacteria doubles each hour, the number of bacteria after t hours can be found by the formula N=3000(2) t . When will the number of bacteria in the culture reach 50,000 ? t= hours (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest ten-thousandth as needed.)

Answer 1

The number of bacteria will reach 50000 after approximately 4.1 hours. This is an example of a mathematical problem using exponential growth.

Step-by-step explanation:

This problem is an example of exponential growth, which is common in areas like Biology and Finance, but it's solved using Mathematics. We can use the given formula N = 3000 * (2^t), where 'N' represents the number of bacteria, '3000' is the initial amount, '2' is the rate of increase, and 't' is time in hours.

To find out when the number of bacteria will reach 50000, we set N = 50000 and solve for 't': 50000 = 3000 * (2^t). By dividing both sides of the equation by 3000, we get an intermediate equation (rounding to ten-thousandths), 16.6667 = 2^t. Using logarithmic functions where the base is 2 (log2), we can calculate the value of t to be approximately about 4.0875. Rounding to the nearest tenth, t = 4.1 hours. So, the number of bacteria will reach 50000 after approximately 4.1 hours.

Learn more about Exponential Growth