The tables show the cat population on two islands over several years. Describe mathematically, as precisely as you can, how the cat population on each island is chan year & 0 & 1 & 2 & 3 & 4 number of cats on Purr Island & 2 & 6 & 10 & 14 & 18 Describe mathematically, as precisely as you can, how the cat population is changing, ex, (added by 5 , subtracted by 2 , multiplied by 4 )

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The tables show the cat population on two islands over several years. Describe mathematically, as precisely as you can, how the cat population on each island is chan year & 0 & 1 & 2 & 3 & 4 number of cats on Purr Island & 2 & 6 & 10 & 14 & 18 Describe mathematically, as precisely as you can, how the cat population is changing, ex, (added by 5 , subtracted by 2 , multiplied by 4 )

Answer 1

The cat population on Purr Island is increasing by 4 each year.

Answer 2

To describe the cat population on Purr Island mathematically, we will analyze the data in the table provided. Observing the progression of the number of cats from Year 0 through Year 4, we can detect a common pattern. It is quite visible that the population of cats on Purr Island is incrementing each year. Given that Year 0 had 2 cats, and every consecutive year had an increment of a fixed number. The difference between each subsequent year’s population value (for example [6-2], [10-6], or [14-10]) seems to look constant, which altogether implies that the growth is linear.To confirm the pattern, let's calculate the differences between the populations of consecutive years:- From Year 0 to Year 1: \(6 - 2 = 4\)- From Year 1 to Year 2: \(10 - 6 = 4\)- From Year 2 to Year 3: \(14 - 10 = 4\)- From Year 3 to Year 4: \(18 - 14 = 4\)The difference is consistently 4 cats per year.

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