Math problem help!?

Question

If the world is now 5.8 billions people and if it continues to grow a the rate of 1.14% compounded continuously. How long will it take before there is only 1 square yard of land per person? Set up ENQ and solve. ( The Earth contains about 1.68 x 10^14 square yards of land)

Answer 1

To solve a compound rate problem, use the following formula:

A = P(1+[r/n])^(n*t) where,

A = final values
P = initial value
r = rate (remember to change into a decimal)
n = # of compounding periods per year
t = time (in years)

Since we are compounding yearly, n = 1 and the equation simplifies to:

A = P(1+r)^t. In this problem, we are solving for t. Here's how you do it:

1) Divide by P on both sides ---------> (A/P) = (1+r)^t
2) Take 'log' of both sides -------> log(A/P) = t*log(1+r)
3) Isolate 't' by ---------> t = [log(A/P)]/[log(1+r)]

plugging in our known values, we can solve for 't'

t = [log(1.68E14/5.8E9)]/[log(1+0.0114)] -----> = about 906 years

----------------

Hope this helps

Answer 2

1.68 x 10^14 / 5.6 x 10^9 = 28,965. 1.14^78.4 = 28,929. Ans: 78.4 years.