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 using the explicit rule to solve.

Answer 1

Hi Jenna,

 

Let's begin by showing a table giving us our answer:

    Year    Population    Calculation

    2000      1,000         initial population

    2015      3,000           1,000 x 3

    2030      9,000           3,000 x 3

    2045    27,000           9,000 x 3

    2060    81,000          27,000 x 3

 

The above table shows a three-fold increase in population every 15 years, according to our given rule.

 

We can express this rule mathematically by this explicit formula for a geometric sequence:

    P(x) = 1000(3)^x where P(x) is the population of Allegheny county after (x) number of 15-year periods.

 

Using this explicit rule, we can get the same answer as shown in our table above:

    P(x) = 1,000(3)^x

        x = 4 (the year 2060 is the end of the 4th 15-year period after the year 2000)

    P(4)  =   1,000(3)⁴

    P(4)  =   1,000(81)

    P(4) = 81,000 (population in 2060)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan (Isaiah 53)