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
.

(1 point)

A coordinate plane's x-axis ranges from 0 to 30 by 5-unit increments and its y-axis ranges from 0 to 6000 by 1000-unit increments. The x-axis is labeled 'Years' and the y-axis is labeled 'Number of Birds.'
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A curve is drawn approximately through the following points: left parenthesis 0 comma 4000 right parenthesis, left parenthesis 6 comma 3000 right parenthesis, left parenthesis 14 comma 2000 right parenthesis, left parenthesis 27 comma 1000 right parenthesis, and left parenthesis 30 comma 850 right parenthesis. An arrow is drawn at the end of the curve pointing downwards.

A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 30 in increments of 1 and 'Number of Birds' on the y-axis ranging from 40,000 to 52,000 in increments of 400. There is an arrow at the decreasing end.
▼Click for Long Desc
The curve is drawn approximately through the following points: left parenthesis 0 comma 48,000 right parenthesis, left parenthesis 6 comma 46,000 right parenthesis, left parenthesis 14 comma 44,000 right parenthesis, left parenthesis 27 comma 42,000 right parenthesis, and left parenthesis 30 comma less than 42,000 right parenthesis.

A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 10 and 'Number of Birds' on the y-axis ranging from 0 to 6000. There is an arrow at the decreasing end.
▼Click for Long Desc
The curve is drawn approximately through the following points: left parenthesis 0 comma 4000 right parenthesis, left parenthesis 2 comma 1000 right parenthesis, left parenthesis 3 comma 600 right parenthesis, left parenthesis 5 comma 200 right parenthesis, left parenthesis 7 comma 0 right parenthesis, left parenthesis 9 comma 0 right parenthesis, and left parenthesis 10 comma 0 right parenthesis.

A curve with a decreasing pattern is plotted on a graph with 'Years' as the x-axis ranging from 0 to 30 in increments of 1 and 'Number of Birds' on the y-axis ranging from 0 to 600 in increments of 20. There is an arrow at the decreasing end.
▼Click for Long Desc
The curve is drawn approximately through the following points: left parenthesis 0 comma 400 right parenthesis, left parenthesis 6 comma 300 right parenthesis, left parenthesis 14 comma 200 right parenthesis, left parenthesis 27 comma 100 right parenthesis, and left parenthesis 30 comma 85 right parenthesis.

Answer 1

First complete the table using y = 4,060(0.95)^t (values rounded to nearest whole bird):

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

These values match the first graph (x-axis 0–30 by 5, y-axis 0–6000 by 1000) — the curve that passes near (0, 4000), (≈6, 3000), (≈14, 2000), (≈27, 1000), (30, 850).