Question

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
0
≤
n
≤
4

(1 point)
Option #
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Answer 1

The function \( n(t) = 50(1.2)^t \) represents the number of bacteria at time \( t \) in hours. In this experiment, the scientist is observing the population of bacteria from \( t = 0 \) hours (when there are 50 bacteria) and checks it specifically at \( t = 4 \) hours.

Given that the scientist is only considering the bacteria growth up to 4 hours, the most relevant and appropriate domain for \( t \) would be from 0 to 4 hours.

Thus, the correct option for the appropriate domain of the problem is:

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