Thread: Relative rate of growth question??

The problem says to use the formula P=P1e^(kt) to fill in the missing vales of k. And P=pop. in the later year, P1=pop. earlier in the year, k=relative growth rate of world pop. per year,t=number of years between the two successive date.The first value is shown k=.28 for 1650. That plus the table below is all the info it gives me.How do I find k for the other years???


Year World population in millions. Relative rate of growth(percent/year)

1650 550 .28
1750 725 k
1850 1175 k
1900 1600 k
1950 2556 k
1980 4458 k
1999 5996 k

Originally Posted by generalsnake

The problem says to use the formula P=P1e^(kt) to fill in the missing vales of k. And P=pop. in the later year, P1=pop. earlier in the year, k=relative growth rate of world pop. per year,t=number of years between the two successive date.The first value is shown k=.28 for 1650. That plus the table below is all the info it gives me.How do I find k for the other years???


Year World population in millions. Relative rate of growth(percent/year)

1650 550 .28
1750 725 k
1850 1175 k
1900 1600 k
1950 2556 k
1980 4458 k
1999 5996 k

I would suggest you post the question exactly as worded.

Also it is unlikely that k ever had a value of 0.28 (which is 28% growth per year) are you confusing percentages with numbers?

CB

Originally Posted by CaptainBlack

I would suggest you post the question exactly as worded.

Also it is unlikely that k ever had a value of 0.28 (which is 28% growth per year) are you confusing percentages with numbers?

CB

alright it says exactly this

Originally Posted by generalsnake

alright it says exactly this

It tells you how to find k, all you need is the starting population the final population and the time.

CB

Originally Posted by CaptainBlack

It tells you how to find k, all you need is the starting population the final population and the time.

CB

I don't get how it works though because it says Po=earlier in the year
and P=later in the year, but I am only given one population for the whole year. And I am supposed to find the rates in the years, not just a year. I tried plugging in the time between the dates but I get some HUGE numbers that surpass the populations that are given.

Originally Posted by generalsnake

I don't get how it works though because it says Po=earlier in the year
and P=later in the year, but I am only given one population for the whole year. And I am supposed to find the rates in the years, not just a year. I tried plugging in the time between the dates but I get some HUGE numbers that surpass the populations that are given.

NO it does not say that it says P0 in the earlier year and P in the later year. So the first k is:

k=(1/(1750-1630)) \ln(725/550)

and what goes in the first blank is 100 times this to make it a % groeth per year.

CB

Originally Posted by CaptainBlack

NO it does not say that it says P0 in the earlier year and P in the later year. So the first k is:

k=(1/(1750-1630)) \ln(725/550)

and what goes in the first blank is 100 times this to make it a % groeth per year.

CB

oh! thank you. I don't know why but I kept seeing earlier in the year, so I had no idea how to solve it .