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)%0D%0AResponses%0D%0A%0D%0A0≤f≤256%0D%0A0 less than or equal to f less than or equal to 256%0D%0A%0D%0A0≤t≤256%0D%0A0 less than or equal to t less than or equal to 256%0D%0A%0D%0A0≤f≤5%0D%0A0 less than or equal to f less than or equal to 5%0D%0A%0D%0A0≤t≤5

Answer 1

To define an appropriate domain for the problem, we need to consider the time frame of Annabel's banana bread baking process. She bakes the banana bread 5 days after returning from the market, which implies that we are interested in the number of days from the time she returned home (which we can denote as \( t = 0 \)) until she bakes the bread (which occurs at \( t = 5 \)).

The function \( f(t) = 8(2)^t \) describes the number of fruit flies as a function of the number of days that have passed. Therefore, the appropriate domain for \( t \) (the time in days) is:

\[ 0 \leq t \leq 5 \]

This indicates that \( t \) starts at 0 (the day she returned home with the bananas) and goes up to 5 (the day she bakes the bread).

So the correct answer is: 0 ≤ t ≤ 5