Question

this table shows the relationship between the bird population in a habitat and the time, in years, since a researcher began tracking the bird population.
determine whether each statement is true. select true or false for each statement.
the bird population increased the same amount each year.
the bird population is always increasing.
the greatest increase in the bird population occurred between year 2 and year 3.

Explanation:

Step1: Calculate the increase in bird population each year

• Year 0 - 1: \(175 - 155=20\)
• Year 1 - 2: \(197 - 175 = 22\)
• Year 2 - 3: \(223-197 = 26\)
• Year 3 - 4: \(251 - 223=28\)
• Year 4 - 5: \(284 - 251=33\)
• Year 5 - 6: \(321 - 284 = 37\)

Since the increases (\(20,22,26,28,33,37\)) are not the same, the statement "The bird population increased the same amount each year" is false.

Step2: Check if the population is always increasing

Since \(155<175<197<223<251<284<321\), the bird population is always increasing. So the statement "The bird population is always increasing" is true.

Step3: Compare the increases

We have the increases: \(20\) (year 0 - 1), \(22\) (year 1 - 2), \(26\) (year 2 - 3), \(28\) (year 3 - 4), \(33\) (year 4 - 5), \(37\) (year 5 - 6). The greatest increase is \(37\) (year 5 - 6), not \(26\) (year 2 - 3). So the statement "The greatest increase in the bird population occurred between year 2 and year 3" is false.

Answer:

• The bird population increased the same amount each year: False
• The bird population is always increasing: True
• The greatest increase in the bird population occurred between year 2 and year 3: False