Question

Complete the input-output table and determine which graph matches the sequence of the decay rate of a specific species of bird modeled by the equation y=4,060(0.94)t

Answer 1

To complete the input-output table, we can choose different values of t and evaluate the corresponding values of y using the equation y = 4,060(0.94)^t. Let's choose t values of 0, 1, 2, 3, and 4.

When t = 0:
y = 4,060(0.94)^0
y = 4,060(1)
y = 4,060

When t = 1:
y = 4,060(0.94)^1
y = 4,060(0.94)
y ≈ 3,819

When t = 2:
y = 4,060(0.94)^2
y = 4,060(0.8836)
y ≈ 3,589

When t = 3:
y = 4,060(0.94)^3
y = 4,060(0.830584)
y ≈ 3,373

When t = 4:
y = 4,060(0.94)^4
y = 4,060(0.77973744)
y ≈ 3,168

Now, let's represent the input-output table:

| t | y |
|---|------|
| 0 | 4,060|
| 1 | 3,819|
| 2 | 3,589|
| 3 | 3,373|
| 4 | 3,168|

Since the decay rate is less than 1 (0.94), we can observe that the population of the bird species is decreasing over time. As t increases, y decreases. Therefore, we are looking for a graph that starts with a high value and continuously decreases.

Considering the options available for the graphs, we can determine that graph option D matches the sequence of the decay rate, where the values gradually decrease over time.