Question

Portland’s population in2007 was about 568 thousand and had been growing by about 1.1% each year

Answer 1

Please make sure to post the whole question next time

a. Write a recursive formula for the population of Portland
b. Write an explicit formula for the population of Portland
c. If this trend continues, what will Portland's population be in 2016?
d. If this trend continues, when will Portland’s population reach 700 thousand?

Answer 2

a) recall that a recursive geometric formula starts by defining the initial value a1, and gives you the term an with respect to the previous term, times r

or in other words, \[a_{n} = (r)a_{n-1} \]

applying this to your problem, a1 is the initial population of 568 thousand, r is the growth ratio (1.1% growth ----> r = 1.011). plug these quantities into the formula to generate the rule.

Answer 3

b) recall that an explicit geometric formula gives you the term an in terms of r, a1, and n (the term #)

\[a_{n}=a_{1}(r)^{n-1}\]
like before, plug in your a1 and r value

Answer 4

c) I strongly recommend using the explicit formula for this, since you won't have to calculate each individual term

n = 1 gives you the initial value (the population in 2007)
9 years later, in 2016, n = 1 + 9 = 10
so plug in n = 10 into the formula and evaluate an

Answer 5

d) again, using the explicit formula, set an = 700 thousand and solve for n. since n represents the # of years after 2006, add 2006 to your result to get the year