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.

Question

A: 0 ≤ f ≤ 256

B: 0 ≤ t ≤ 256

C: 0 ≤ t ≤ 5

D: 0 ≤ f ≤ 5

Answer 1

To define an appropriate domain for the problem, we need to consider the timeframe in which Annabel is monitoring the growth of the fruit flies, which is from the time she returns from the market until she bakes the banana bread 5 days later.

The function given is \( f(t) = 8(2)^t \), where \( t \) is the number of days after her return from the market.

Since Annabel bakes the banana bread 5 days after returning home, the appropriate values for \( t \) (the number of days) will be from \( t = 0 \) (the day she returns with the bananas) to \( t = 5 \) (the day she bakes the banana bread).

Thus, the appropriate domain for \( t \) is: \[ 0 \leq t \leq 5 \]

Therefore, the correct answer is:

C: 0 ≤ t ≤ 5