A scientist observes a population of bacteria in a petri dish. The population grows exponentially, doubling every 2 hours. After 4 hours of observation, there are about 6,000 bacteria. Which equation can you use to estimate n, the number of bacteria that were originally in the petri dish? A. n^2 = 6,000 B. 2n = 6,000 C. 4n = 6,000 D. 6,000(2)^4 = n E. 6,000(2)^2 = n F. 8n = 6,000
We can use the formula for exponential growth to estimate the original number of bacteria, which is given by the equation P = P0 * (2^(t/h)), where P is the final population, P0 is the initial population, t is the time elapsed, and h is the doubling time.
In this case, P = 6,000 (the final population after 4 hours), t = 4 hours, and h = 2 hours (doubling time).
Plugging these values into the equation, we get:
6,000 = P0 * (2^(4/2))
Simplifying, we have:
6,000 = P0 * (2^2)
So the correct equation to estimate n, the number of bacteria that were originally in the petri dish, is E. 6,000(2)^2 = n.