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
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
0
≤
𝑡
≤
104

Option #2: 0≤n≤104
0
≤
𝑛
≤
104

Option #3: 0≤t≤4
0
≤
𝑡
≤
4

Option #4: 0≤n≤4

Answer 1

To determine the appropriate domain for the problem, we need to consider the context of the equation provided. The equation \( n(t) = 50(1.2)^t \) calculates the number of bacteria \( n \) after \( t \) hours.

Given that the scientist is checking the population after 4 hours, the variable \( t \) represents time in hours and should be non-negative. Thus, the reasonable range for \( t \) would be between \( 0 \) and \( 4 \) hours, which corresponds to the time the bacteria are being observed.

Therefore, the appropriate domain for the problem, given the context, would be:

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

It indicates the range of time over which the observation is made. Options #1, #2, and #4 do not correctly reflect the appropriate domain for the variable \( t \) in the context of checking the population after 4 hours.