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9) Given a 2021 world population growth rate of about 1.03% per year, how long would it take for the world's

population to double? By what year would this doubling occur?

User Alpheus
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1 Answer

4 votes

Step-by-step explanation:

p0 = world population in 2021

p = actual world population =

= p0 × (1.03)^(x - 2021)

with x being the year.

for p to double from p0 to 2×p0 that means that we need to find the value of x for which

(1.03)^(x - 2021) = 2

log1.03((1.03)^(x - 2021) = log1.03(2)

x - 2021 = log1.03(2)

x = log1.03(2) + 2021

remember,

loga(b) = logc(b)/logc(a)

I love my log10, so c = 10 :

x = log(2)/log(1.03) + 2021 =

= 0.301029995.../0.012837225... + 2021 =

= 23.44977225... + 2021 = 2,044.449772...

the doubling would occur in the middle between 2044 and 2045, so, during the year 2044.

User Mrbrdo
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8.3k points