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?

Answer 1

To analyze the function \( f(t) = 8(2)^t \) for \( t \) ranging from 0 to 6 (representing the first 6 days), we can calculate the values of \( f(t) \) for each day.

1. For \( t = 0 \):
\[
f(0) = 8(2)^0 = 8(1) = 8
\]

2. For \( t = 1 \):
\[
f(1) = 8(2)^1 = 8(2) = 16
\]

3. For \( t = 2 \):
\[
f(2) = 8(2)^2 = 8(4) = 32
\]

4. For \( t = 3 \):
\[
f(3) = 8(2)^3 = 8(8) = 64
\]

5. For \( t = 4 \):
\[
f(4) = 8(2)^4 = 8(16) = 128
\]

6. For \( t = 5 \):
\[
f(5) = 8(2)^5 = 8(32) = 256
\]

7. For \( t = 6 \):
\[
f(6) = 8(2)^6 = 8(64) = 512
\]

Now, we summarize the results:

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

Next, we observe that this function is an exponential growth function. The number of fruit flies doubles each day, starting from 8 flies on day 0.

When you plot the points \( (0, 8), (1, 16), (2, 32), (3, 64), (4, 128), (5, 256), (6, 512) \), you would expect to see a steep upward curve, illustrating exponential growth.

As I cannot directly provide or visualize graphs here, you should look for a graph that starts at 8, rises quickly, and follows the doubling pattern mentioned, effectively growing from the initial 8 fruit flies to 512 by the end of the 6th day.

If you are provided with multiple graphs to compare, select the one that demonstrates this exponential growth characteristic.