According to the National Census, the population of the District of Columbia con

Question

According to the National Census, the population of the District of Columbia consisted of 601,767 people in 2010, larger than both the states of Wyoming and Vermont. The third-least-populous state in the U.S. is Alaska, with its population for three separate years given in the table below:

1.      (a) Is the table above well approximated by either a linear or exponential function? If so, give an equation for a function that could represent the approximate population of Alaska in terms of the number of years since 2010.

2.      (b) If the population of D.C. is growing at a rate of 2% per year, give an equation for the population as a function of the number of years since 2010.

3.      (c) Assuming that these two equations hold, will the population of D.C. ever surpass the population of Alaska? If so, in what year and month will this happen?

Explanation / Answer

(726750 - 712500) / (2013 - 2010), i.e 4750

And

(741285 - 726750) / (2013 - 2010), i.e 4845

These slopes are very close but not equal

So, exponential is the best, yo!

(0,712500)
(3,726750)
(6,741285)

We get
P = 712500e^(0.006609t) ---> ANS

---------------------------------------------------

b)
Growin' at 2% per year

So, rate = 1 + 2% i.e 1.02

So, A = P(1 + r)^t

A = P(1.02)^t

A = 601767(1.02)^t -----> ANS

---------------------------------------------------

c)
601767(1.02)^t ---> DC population

712500e^(0.006609t) ---> Alaska population

We need
601767(1.02)^t > 712500e^(0.006609t)

We find t = 12.802

So, after approx 13 yrs,
i.e in 2023 ---> ANS

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