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

so my guess is that you would start with what ya got

2008 560-4%
2009 559.96-4%
2010 559.92-4%
(continue til you get to 2020)
sooo;
a.) 559.92
b.) 559.52

If the population declines at 4%, it means that the surviving population is 96% of the previous year.

In the summer of 2008, there were 560 pairs. So in the summer of 2009, there were 560*(96/100)
= 537.6 pairs (theoretically)
= 538 pairs

In the summer of 2009, the population declined again to 96% of the theoretical population of 2008, thus
537.6*(96/100)
=516.1 pairs (theoretically)
= 516 pairs (rounded)

To calculate the number of pairs of cuckoos in the area in the summer of 2009 and 2020, we need to use the given information about the population decline rate.

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

Step 1: Calculate the decline in population:
Decline = 4% of 560
Decline = (4/100) * 560
Decline = 0.04 * 560
Decline = 22.4

Step 2: Subtract the decline from the initial population:
Population in 2009 = Initial population - Decline
Population in 2009 = 560 - 22.4
Population in 2009 = 537.6

Therefore, the number of pairs of cuckoos in the area in the summer of 2009 is approximately 537.6.

(b) To calculate the number of pairs of cuckoos in the area in the summer of 2020, we need to calculate the decline in population for each year from 2008 to 2020.

Step 1: Calculate the decline in population for each year:
Decline per year = 4% * Initial population

Step 2: Subtract the total decline from the initial population:
Population in 2020 = Initial population - (Decline per year * Number of years)

Population in 2020 = 560 - (0.04 * 560 * 12)

Population in 2020 = 560 - (0.04 * 6720)

Population in 2020 = 560 - 268.8

Population in 2020 = 291.2

Therefore, the number of pairs of cuckoos in the area in the summer of 2020 is approximately 291.2.