Question

Annabel wants to make banana bread for the bake sale. She went to the market to buy bananas, and she noticed fruit flies after she returned home with her produce. The number of fruit flies grows at an exponential rate modeled by the equation f(t)=8(2)t
, where f is the number of fruit flies after t days. Define an appropriate domain for the problem if Annabel bakes the banana bread 5 days after returning from the market.(1 point)
Responses

0≤t≤256
0 less than or equal to t less than or equal to 256

0≤t≤5
0 less than or equal to t less than or equal to 5

0≤f≤5
0 less than or equal to f less than or equal to 5

0≤f≤256

Answer 1

In this scenario, Annabel is concerned with the growth of fruit flies over a period of time leading up to when she bakes the banana bread. The function \( f(t) = 8(2)^t \) models the number of fruit flies after \( t \) days, with \( t \) representing the number of days since she returned from the market.

Since Annabel bakes the banana bread 5 days after returning from the market, the value of \( t \) should reflect this time frame. An appropriate domain for the variable \( t \) in this context would be from the moment she brings the bananas home (day 0) until the day she bakes the banana bread (day 5).

Thus, the appropriate domain is:

\[ 0 \leq t \leq 5 \]

So the correct response is:

**0 ≤ t ≤ 5**