Question

In 1996, Town M had a population of 30,500 people, and it has grown at a rate of 2% every year. In 1996, Town N had 32,500 people and the population has increased by a constant rate of 600 people each year. In what year were the populations of the two towns approximately equal?

Answer 1

Answer:

18 years after 1996 which is 2014

Step-by-step explanation:

Town M had a population of 30,500 people. It grows by 2%. That means the next year will be 30,500+0.02(30,500)=31,110. The next year will be 31,110+0.02(31110)=31732.2 and so forth.

Town N had 32,500 and grows by 600 each year. That means the next year will be 32,500+600=33,100. The next year will be 33,100+600=33,700 and so forth.

Year      Town M       Town N

1            31,110            33,100

2           31,732.2       33,700

3           32366.8       34, 300

4           33014.2        34,900

5           33674.5       35,500

6           34348          36,100

7           35035          36,700

We can see the populations are getting closer but not very fast. Let's try higher numbers.

Year 20 gives 45,321 and 44,500.  We are close. Let's try year 18. We get 43,561.5 and 43,300.