Suppose that at one time the population of an idyllic Caribb

Suppose that at one time, the population of an idyllic Caribbean island equaled 1,000 people and remained constant for years. Howev er, when word spread about how great life was on the island, people began moving there in droves. Beginning with \"Year 1\'\', the island population has increased by 250 additional people per year a. ress the island population in year n (Pn) as an arithmetic sequence. Exp Poperation in the first 250 en population in the nt rear lado t 250n looo t 250n b. Graph the annual island population between yearsothrough 10. c. Graph the annual rate of change in the island population between years 1 through 10 d. Does the annual rate of change in the island population increa se, decrease or remain constant over time?

Solution

a)
Pn = 1000 + 250n is correct
as in the first yr itself an extra 250 get on the island

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b) Graph :

You\'ve already graphed it.
IT seems perfect

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c) Annual rate of change :
Pn = 1000 + 250n

With each yr, 250 get added on

So, annual rate of change is :
An increase of 250 people per year

So, the graph would just be a constant horizontal line
at 250 parallel to the x-axis
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d) Constant rate of change as with each yr, a constant 250 get added

So, rate of change is a constant 250 people per year