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, there 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

Answer 1

In this case, the function \( n(t) = 50(1.2)^t \) represents the number of bacteria after \( t \) hours. The variable \( t \) represents time, measured in hours, and since time cannot be negative in this context, the appropriate domain for \( t \) would be non-negative values.

Thus, the appropriate domain for the function \( n(t) \) would be:

\[ t \geq 0 \]

In interval notation, this can be expressed as:

\[ [0, \infty) \]

This means that the scientist can observe the population starting from time \( t = 0 \) (the initial population) and continuing for as long as needed (including the 4-hour mark).