SOLUTION: How long will it take for the population of China to reach 7237615800. The starting population was 562579779. The growth rate is 1.566658 percent annually.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How long will it take for the population of China to reach 7237615800. The starting population was 562579779. The growth rate is 1.566658 percent annually.      Log On


   

Question 964182: How long will it take for the population of China to reach 7237615800. The starting population was 562579779. The growth rate is 1.566658 percent annually.
Answer by Theo(13342) About Me  (Show Source):
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the current population of china is 562579779.
the projected population of china is 7237615800.
the growth rate is 1.566658 percent annually.

the formula would be fv = pv * (1+i)^n
fv is the future value which is the projected population of china.
pv is the present value which is tyhe current population of china.
i is equal to .01566658 which is the percent growth rate per year divided by 100.

the formula becomes:
7237615800 = 562579779 * (1.01566658)^n

n is the number of years.

divide both sides of this equation by 562579779 to get:

7237615800 / 562579779 = (1.01566658)^n

take the log of both sides of the equation to get:

log(7237615800 / 562579779) = log((1.01566658)^n)

since log(a^n) = n*log(a), your equation becomes:

log(7237615800 / 562579779) = n * log(1.01566658)

divide both sides of this equation by log(1.01566658) to get:

log(7237615800 / 562579779) / log(1.01566658) = n

solve for n to get:

n = 164.3278458 years.