Question

Byron bought some bananas at the store and noticed some fruit flies after returning home. The number of fruit flies can be modeled by the equation f(t)=8(2)t
where f is the number of fruit flies after t days. Which graph models the number of fruit flies over the first 6 days?(2 points)
Responses

Answer 1

To determine the graph that models the number of fruit flies over the first 6 days using the equation \( f(t) = 8(2)^t \), we can calculate the values of \( f(t) \) for \( t \) from 0 to 6 days.

Let's calculate \( f(t) \) for each of these values:

- \( f(0) = 8(2)^0 = 8(1) = 8 \)
- \( f(1) = 8(2)^1 = 8(2) = 16 \)
- \( f(2) = 8(2)^2 = 8(4) = 32 \)
- \( f(3) = 8(2)^3 = 8(8) = 64 \)
- \( f(4) = 8(2)^4 = 8(16) = 128 \)
- \( f(5) = 8(2)^5 = 8(32) = 256 \)
- \( f(6) = 8(2)^6 = 8(64) = 512 \)

Now, the number of fruit flies grows exponentially. Here are the calculated values:

- Day 0: 8
- Day 1: 16
- Day 2: 32
- Day 3: 64
- Day 4: 128
- Day 5: 256
- Day 6: 512

The graph should show an exponential growth, starting at 8 and rapidly increasing as the days progress.

The key points to look for in the graph:

- Starts at (0, 8)
- (1, 16), (2, 32), (3, 64), (4, 128), (5, 256), and (6, 512)
- The curve will steeply rise after each day.

As you compare the graphs, select one that aligns with these calculated points and exhibits the upward exponential trend over the 6 days.