HELP: Population

**dc52789** · October 25th 2008, 08:20 PM

If the world population is now 6.2 billion people and if it continues to grow at an annual rate of 1.25% compounded continuously, how long (to the nearest year) will it take before there is only 1 square yard of land per person? (The Earth contains approximately 1.68 x 10^14 square yards of land)

**Jhevon** · October 25th 2008, 08:31 PM

Originally Posted by dc52789

If the world population is now 6.2 billion people and if it continues to grow at an annual rate of 1.25% compounded continuously, how long (to the nearest year) will it take before there is only 1 square yard of land per person? (The Earth contains approximately 1.68 x 10^14 square yards of land)

you must use the same formula for exponential growth that i gave you last time.

$P(t) = P_0 e^{rt}$

you want the time when $P(t) = 1.68 \times 10^{14}$

**dc52789** · October 25th 2008, 08:44 PM

Originally Posted by Jhevon

you must use the same formula for exponential growth that i gave you last time.

$P(t) = P_0 e^{rt}$

you want the time when $P(t) = 1.68 \times 10^{14}$

How about the 1.25% and the 6.2 billion people? Are they part of the formula?

**Jhevon** · October 25th 2008, 09:12 PM

Originally Posted by dc52789

How about the 1.25% and the 6.2 billion people? Are they part of the formula?

1.25% means the rate of growth is 0.0125, the 6.2 billion is the $P_0$

**dc52789** · October 25th 2008, 09:24 PM

Originally Posted by Jhevon

1.25% means the rate of growth is 0.0125, the 6.2 billion is the $P_0$

So...how do we write that up in exponential growth formula?
P(t) = 6.2 e^0.0125t?

**Jhevon** · October 25th 2008, 09:29 PM

Originally Posted by dc52789

So...how do we write that up in exponential growth formula?
P(t) = 6.2 e^0.0125t?

yes, if you note that $P_0$ is in the units of billions. you must also note that this will change what you want P(t) to end up being as well.

**dc52789** · October 25th 2008, 09:44 PM

Originally Posted by Jhevon

yes, if you note that $P_0$ is in the units of billions. you must also note that this will change what you want P(t) to end up being as well.

Is the answer around 632 years?

**Jhevon** · October 25th 2008, 09:49 PM

Originally Posted by dc52789

Is the answer around 632 years?

nope, i got 817

**dc52789** · October 25th 2008, 09:51 PM

Originally Posted by Jhevon

nope, i got 817

How did you get 817?

**Jhevon** · October 25th 2008, 09:55 PM

Originally Posted by dc52789

How did you get 817?

$1.68 \times 10^{14} = 6.3 \times 10^9e^{0.0125t}$ and solve for $t$

**dc52789** · October 25th 2008, 10:06 PM

Originally Posted by Jhevon

$1.68 \times 10^{14} = 6.3 \times 10^9e^{0.0125t}$ and solve for $t$

now I got it.

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