Use the table to answer the question. 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)ty=4,060(0.95)t . (1 point) Responses Image with alt text: 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. Image with alt text: 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.' Image with alt text: 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. Image with alt text: 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. Skip to navigation Item 1 , Fully Attempted. Item 2 , Fully Attempted. Item 3 , Unattempted. Item 4 , Unattempted. Item 5 , Unattempted. Previous Next

Answer 1

To determine which graph matches the sequence of the decay rate of the bird species modeled by the equation \( y = 4,060(0.95)^t \), we first complete the input-output table by calculating the number of birds at each of the given years.

Using the formula \( y = 4,060(0.95)^t \):

1. For \( t = 0 \): \[ y = 4,060(0.95)^0 = 4,060(1) = 4,060 \]

2. For \( t = 5 \): \[ y = 4,060(0.95)^5 \approx 4,060(0.7738) \approx 3,137.43 \approx 3,137 \]

3. For \( t = 10 \): \[ y = 4,060(0.95)^{10} \approx 4,060(0.5987) \approx 2,426.46 \approx 2,426 \]

4. For \( t = 15 \): \[ y = 4,060(0.95)^{15} \approx 4,060(0.4633) \approx 1,882.38 \approx 1,882 \]

5. For \( t = 20 \): \[ y = 4,060(0.95)^{20} \approx 4,060(0.3487) \approx 1,415.36 \approx 1,415 \]

Now we can summarize the values in the table:

| Years (t) | Number of Birds (y) | |-----------|----------------------| | 0 | 4,060 | | 5 | 3,137 | | 10 | 2,426 | | 15 | 1,882 | | 20 | 1,415 |

Now, let's identify the right graph among the options provided. Since we need a graph that shows the exponential decay over 20 years and the number of birds dropping significantly, the appropriate choice would be the graph that:

• Shows the number of birds starting around 4,000 and decreasing steadily.
• Clearly indicates the lower range of the number of birds (as the values calculated decline quickly).

From the descriptions of the graphs you provided, look for the graph that best fits these criteria, specifically one that aligns with the rapid decay observed in the calculations and retains the significant drop in bird population over time while being bounded (not extending excessively beyond 5,000 or less than 0).

Based on the decay factor and calculated values, the most suitable graph would likely be the one that has a more zoomed-in focused look on the y-axis (between 0 and 6,000) or perhaps explicitly ranges closer to the calculated values (1,000 to 5,000). Look for a graph that reflects these characteristics to make your selection accordingly.