Answer to Question #277234 in Algebra for abcde

Question

Using the world population formula P = 6.9(1.011)t, where t is the number of

years after 2010 and P is the world population in billions of people, estimate:

a) the population in the year 2030 to the nearest hundred million, and

b) by what year will the population be double from 2010?

Answer 1

$P = 6.9(1.011)^t$

a)

$t=2030-2010=20(years)$

$P = 6.9(1.011)^{20}=8.6$

The world population will be 8.6 billions of people in 2030.

b)

$P(t_1) = 6.9(1.011)^{t_1}=2(6.9)$

$(1.011)^{t_1}=2$

$t_1=\dfrac{\ln2}{\ln1.011}$

$t_1=63.36\ years$

$2010+64=2074$

The population will be double by 2074.