A bacterium can divide every 20 minutes. Beginning with a single individual, how many bacteria will be there in the population if there is exponential growth for 3 hours?
**Core Concept**
The question is testing the concept of exponential growth, specifically in the context of bacterial populations. Exponential growth occurs when a population's size increases at a rate proportional to its current size, resulting in a rapid increase in population size over time.
**Why the Correct Answer is Right**
To solve this problem, we need to use the formula for exponential growth: N(t) = N0 * e^(kt), where N(t) is the population size at time t, N0 is the initial population size, e is the base of the natural logarithm, and k is the growth rate. In this case, the initial population size is 1 bacterium, and the growth rate is 1/20 (since the bacterium divides every 20 minutes). We need to find the population size after 3 hours (180 minutes). Since we are dealing with exponential growth, we can use the formula N(t) = N0 * e^(kt) and calculate the population size at t = 180 minutes.
**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not take into account the exponential growth of the bacterial population. Exponential growth results in a rapid increase in population size over time, so the population size will be much larger than 2.
* **Option B:** This option is incorrect because it does not take into account the continuous nature of exponential growth. The population size does not increase in discrete steps, but rather continuously over time.
* **Option D:** This option is incorrect because it does not take into account the growth rate of the bacterial population. The growth rate is 1/20, which means the population size will increase by a factor of 2 every 20 minutes.
**Clinical Pearl / High-Yield Fact**
A key concept to remember is that exponential growth results in a rapid increase in population size over time. This can be described by the formula N(t) = N0 * e^(kt), where N(t) is the population size at time t, N0 is the initial population size, e is the base of the natural logarithm, and k is the growth rate.
**Correct Answer: C. 2^(180/20) = 2^9 = 512**