Thread: HELP: Population

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)

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.

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

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

Originally Posted by Jhevon

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

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

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

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

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 $\displaystyle P_0$

Originally Posted by Jhevon

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

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

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 $\displaystyle P_0$ 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.

Originally Posted by Jhevon

yes, if you note that $\displaystyle P_0$ 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?

Originally Posted by dc52789

Is the answer around 632 years?

nope, i got 817

Originally Posted by Jhevon

nope, i got 817

How did you get 817?

Originally Posted by dc52789

How did you get 817?

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

Originally Posted by Jhevon

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

now I got it.