the population of allegheny county triples every 15 years. If the population in the year 2000 is 1000 what will the population be in the year 2060?

Question

showing a table and explicit rule to solve the problem

Answer 1

Hello Jenna,

Here is the solution to the problem:

 

Given that the population triples every 15 years, we can write this in form of an equation

--> 2000 + 15.y

where y = 1, 2, 3, 4... (first fifteen years, second fifteen years, third fifteen years, fourth fifteen years, and so on)

 

Since population triples every fifteen years, we can write

--> 3.p

i.e. for the given population of an year, the new population would be three times of what it was.

 

Thus we have a relationship for the year and the population:

Year                   Population

2000 + 15.y        3.p

 

We can now show a table for values y = 1, 2, 3, .. (till we reach year = 2060); the corresponding year, and the population (which initially p = 1000)

 

Value of y                Year (2000 + 15.y)                  Population (3.p)

1                              2000 + 15(1) = 2015                  3(1000) = 3000

2                              2000 + 15(2) = 2030                  3(3000) = 9000

3                              2000 + 15(3) = 2045                  3(9000) = 27,000

4                              2000 + 15(4) = 2060                  3(27,000) = 81,000

 

Since we have reached the year 2060, we stop with the calculations.

 

Hence the population in the year 2060 = 81,000.

 

 

Hope it answers your question.

You can get back to me for any doubts.

 

Thanks.