Question

the table shows two sloth populations growing over time. these patterns continued for many years. based on this information, fill in the extra rows in the table. time (years since 1990) population 1 (thousands) population 2 (thousands) 0 90.0 39 1 76.5 37 2 65.0 35 3 55.3 33 4 47.0 31 5 6 7 8

Explanation:

Step1: Find the pattern for population 1

For population 1, from year 0 to 1, the change is $90.0 - 76.5=13.5$, from year 1 to 2, the change is $76.5 - 65.0 = 11.5$, from year 2 to 3, the change is $65.0-55.3 = 9.7$, from year 3 to 4, the change is $55.3 - 47.0=8.3$. The differences $13.5,11.5,9.7,8.3$ are decreasing by approximately 2 each time.

Step2: Calculate population 1 values

For year 5: The decrease from year 4 to 5 should be around $8.3 - 2=6.3$. So population 1 is $47.0-6.3 = 40.7$.
For year 6: The decrease from year 5 to 6 should be around $6.3 - 2 = 4.3$. So population 1 is $40.7-4.3=36.4$.
For year 7: The decrease from year 6 to 7 should be around $4.3 - 2=2.3$. So population 1 is $36.4 - 2.3=34.1$.
For year 8: The decrease from year 7 to 8 should be around $2.3 - 2 = 0.3$. So population 1 is $34.1-0.3=33.8$.

Step3: Find the pattern for population 2

For population 2, the population decreases by 2 each year.

Step4: Calculate population 2 values

For year 5: $31-2 = 29$.
For year 6: $29 - 2=27$.
For year 7: $27-2 = 25$.
For year 8: $25-2=23$.

Answer:

time (years since 1990)	population 1 (thousands)	population 2 (thousands)
6	36.4	27
7	34.1	25
8	33.8	23