In the summer of 2008 the population of cuckoos in an area was estimated as 560 pairs. If the numbers returning are declining at 4% each year, calculate

(a) the number of pairs of cuckoos in the area in the summer of 2009;
(b) the number of pairs of cuckoos in the area in the summer of 2020.

pairs = 560* .96^(year-2008)

2(x-3)< 4x+10

To calculate the number of pairs of cuckoos in the area in the summer of 2009 and 2020, we need to apply the declining rate of 4% to the given population and calculate the new population each year.

(a) To calculate the number of pairs of cuckoos in the area in the summer of 2009, we need to apply the 4% decline rate to the initial population of 560 pairs.

Step 1: Calculate the decline in population for one year:
Decline = 4% of 560 pairs
Decline = 0.04 * 560 pairs
Decline = 22.4 pairs

Step 2: Subtract the decline in population from the initial population to get the population in the summer of 2009:
Population in 2009 = Initial population - Decline
Population in 2009 = 560 pairs - 22.4 pairs
Population in 2009 = 537.6 pairs

Therefore, the estimated number of pairs of cuckoos in the area in the summer of 2009 is approximately 537.6 pairs (rounded to the nearest pair).

(b) To calculate the number of pairs of cuckoos in the area in the summer of 2020, we need to continue applying the 4% decline rate to the population each year, starting from the population in 2009.

Step 1: Repeat the decline calculation for each year from 2009 to 2020:
Decline in 2010 = 4% of 537.6 pairs
Decline in 2011 = 4% of (initial population - decline in 2010)
Repeat this calculation for each subsequent year until 2020.

Step 2: Subtract the respective declines each year from the previous year's population to get the population in the following year.
For example:
Population in 2010 = Population in 2009 - Decline in 2010
Population in 2011 = Population in 2010 - Decline in 2011
Continue this calculation for each subsequent year.

To simplify the process, you can use a spreadsheet or a calculator with a loop function to perform the calculations automatically starting from the population in 2009. This will allow you to determine the population in the summer of 2020.

Note: Please note that the population estimate in 2020 will be an approximation based on the given decline rate. There may be other factors that can affect the actual population of cuckoos in the area.