A few days ago
Math question?
given that current world population is 6.45 * 10^9 and increasing at the rate of 1.14% per year, calculate the number of years it would take for the world population to double at the current rate
Top 2 Answers
A few days ago
Favorite Answer
(6.45*10^9)*(1.0114)^n = 12.9*10^9
>>>>>>>>>(1.0114)^n = 2
>>>>>>>>>>>>log|1.0114|(2) = n
>>>>>>>>>>>>>>>>>>>>n = 61.148… years
0
A few days ago
If the present population is P and the growth rate is 1.14% per year, then next year the population will be P + .0114P = 1.0114P, since 1.14% = .0114. In two years the population will be (1.0114)(1.0114)P, in three years it will be (1.0114)(1.0114)(1.0114)P, etc.
Thus in n years the population will be ((1.0114)^n)P.
We are interested in how long it takes for the population to double; that is, what is n when (1.0114)^n = 2?
Take the logarithms of both sides.
log((1.0114)^n) = n log(1.0114) = log 2
So n = log 2 / log (1.0114) = .30103 / .00492 = 61.1
The population will double in just a little more than 61 years.
Notice that the actual population does not matter. Any population with a growth rate of 1.14% a year will double in about 61 years.
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