The following functions give the population of three towns in terms of the number of years, t, since 1995. Use this information to answer the following questio

Question

Let L represent the population of Linwood where L=9156(1.06)^t

Let N represent the population of Northfield where B=7534(1.14)^t

 

Let S represent the population of Somers Point where S=13972(0.87)^t

 

QUESTIONS:

1. In what year was the population of Linwood predicted to be 9850 people?

2. In what year was the population of Northfield predicted to be 13,400 people?

3. In what year was the population of Somers Point predicted to be 11,220 people?

 

Answer 1

I can show you the method for question 1, and then hopefully you can fill in the rest!

 

Our model for the population of Linwood is:

L=9156(1.06)^t

So if for some unknown time point t, we have L=9850, we can simply set our model above equal to 9850 and solve for t.

9850 = 9156(1.06)^t

9850/9156 = (1.06)^t

To isolate t, we need to remove it from the exponent. To do this, we take the natural log of both sides. When t is an exponent inside of the log, we can pull it out of the log as a constant multiplier. 

[Remember b*ln(a) = ln(a^b)]

ln(9850/9156) = ln(1.06^t) = t*ln(1.06)

 

Hence, t = ln(9850/9156) / ln(1.06). Plug this into your calculator and you are set!