Question

A scientist is observing a particular species of bacteria growing in a petri dish. The number of bacteria can be represented by the equation n(t)=50(1.2)t , where n is the number of bacteria after t hours. If the scientist checks the population in 4 hours, what would be an appropriate domain for the problem? Option #1: 0≤t≤104 Option #2: 0≤n≤104 Option #3: 0≤t≤4 Option #4: 0≤n≤4 (1 point) Option #()

Answer 1

To determine the appropriate domain for the problem, we need to focus on the variable \( t \), which represents time in hours. Since the scientist is observing the bacteria for a duration of 4 hours, the relevant range for \( t \) is from 0 to 4.

Now let's evaluate the options:
- **Option #1: \( 0 \leq t \leq 104 \)** - This includes values far beyond what the scientist is checking, which is not relevant here.
- **Option #2: \( 0 \leq n \leq 104 \)** - This describes the population of bacteria, but it is not specifically about the time variable \( t \).
- **Option #3: \( 0 \leq t \leq 4 \)** - This directly corresponds to the time period during which the scientist is observing the bacteria and is completely appropriate.
- **Option #4: \( 0 \leq n \leq 4 \)** - Similarly, this describes a range for the number of bacteria but is not relevant to the time variable.

Thus, the correct option reflecting the appropriate domain for \( t \) in this context is:

**Option #3: \( 0 \leq t \leq 4 \)**.