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Question

according to statistics canada, Chestermere, Alberta is one of the fastest growing communities in canada. between 2001 to 2006, the population grew an average rate of about 8 percent per year.

(A) the population of Chestermere in 2001 was 6462. Determine the population for the years 2002 to 2004, inclusive.

(B) write a general term of the geometric sequence that models the population of Chestermere, where n is the number of years starting in 2001.

(C) predict the population if Chestermere in 2020

Please help

Thank you so much!

Answer 1

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Geometric series like this are defined by a start term and a common ratio. The start term here is 6462, the common ration is 1.08.

The nth term of a progression is given by arⁿ⁻¹ where a is the start term and r is the ratio.

A)

2001 = 6462

2002 = 6462 * 1.08 = 6979

2003 = 6979 * 1.08 = 7537

2004 = 7537 * 1.08 = 8140

B) nth term = 6462 * 1.08ⁿ⁻¹

C) n = 20. 6462 * 1.08^19 = 27888