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.