A bacteria culture starts with 200 bacteria and in 1 hour contains 400 bacteria. How many hours does it take to reach 2000 bacteria?

Question

Quizplus · Accepted Answer

The bacteria culture doubles every hour. To find the number of hours it takes to grow from 200 to 2000 bacteria, we can use the formula for exponential growth: $N = N_0 \cdot 2^t$, where $N$ is the final amount, $N_0$ is the initial amount, and $t$ is the time in hours. Rearranging to solve for $t$, we get $t = \log_2 \frac{N}{N_0}$. Substituting $N = 2000$ and $N_0 = 200$, we get $t = \log_2 \frac{2000}{200} = \log_2 10$. Since $\log_2 10$ is equivalent to $\frac{\ln 10}{\ln 2}$, the correct answer is H.

A Bacteria Culture Starts with 200 Bacteria and in 1 ln⁡400\ln 400ln400

A Bacteria Culture Starts with 200 Bacteria and in 1 $\ln 400$