Question

Use the table to answer the question.

Make the table like the one to determine the decay rate of birds in 20 years.
Years (t) 0 5 10 15 20
Number of Birds (y)
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(0.95)t
.

Answer 1

First fill the table using y = 4,060(0.95)^t (t in years).

Years (t) | Number of birds (y)
0 -> 4,060
5 -> 4,060(0.95^5) ≈ 3,142
10 -> 4,060(0.95^10) ≈ 2,431
15 -> 4,060(0.95^15) ≈ 1,881
20 -> 4,060(0.95^20) ≈ 1,455

Notes about the matching graph:
- This is an exponential decay curve starting at 4,060 (t = 0) and decreasing toward 0.
- It falls quickly at first and then levels off (concave up toward the horizontal axis).
- If you have multiple graph choices, pick the one that shows a smooth exponential decrease through roughly the points above (4060, 3142, 2431, 1881, 1455).