Question 964182
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.