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?

Question

Option #1: 0 ≤ t ≤ 104

Option #2: 0 ≤ n ≤ 104

Option #3: 0 ≤ t ≤ 4

Option #4: 0 ≤ n ≤ 4

Answer 1

To determine the appropriate domain for the problem, we need to consider what the variable \( t \) represents in the context of the bacteria growth equation \( n(t) = 50(1.2)^t \). Here, \( t \) is the time in hours, and we are interested in observing the number of bacteria after a specific duration.

Given that the scientist is checking the population in 4 hours, the relevant values for \( t \) should range from the start (0 hours) up to the point of observation (4 hours). Therefore, the appropriate domain for \( t \) should be represented as all values from 0 to 4 hours.

Among the provided options, the one that matches this reasoning is:

Option #3: 0 ≤ t ≤ 4

Options #1 and #2 do not match because they extend beyond the specified time frame of observation. Option #4 is incorrect as it represents a range for \( n \), not \( t \).