Question

World population is approximately upper p equals 6.4 left-parenthesis 1.0126 right-parenthesis superscript t, with upper p in billions and t in years since 2004. (a) what is the yearly percent rate of growth of the world population? The percent rate of growth is entry field with incorrect answer now contains modified data % per year. (b) what was the world population in 2004? The world population in 2004 was entry field with correct answer 6.4 billion people. What does this model predict for the world population in 2018? Round your answer to two decimal places. The predicted world population in the year 2018 is entry field with incorrect answer billion people. (c) use part (b) to find the average rate of change of the world population between 2004 and 2018. Round your answer to the nearest integer. The average rate of change of the world population between 2004 and 2018 is about entry field with incorrect answer million people per year.

Answer 1

Given equation is

$P=6.4(1.0126)^t$

It gives approx world population in billions for t years since 2004.

Answer(a):

Compare with growth formula P=a(b)^t, we get:

growth factor b = 1.0126

We know that if r is the percent rate of growth then

1+r=b

1+r=1.0126

r=0.0126

Hence the yearly percent rate of growth of the world population is 0.0126 or 1.26%.

Answer(b):

To find worlds population in 2004, plug t=0 because year is counted from 2004.

$P=6.4(1.0126)^0 = 6.4*1 = 6.40$

Hence answer is 6.40 billion.

To find worlds population in 2018, plug t=2018-2004=14 because year is counted from 2004.

$P=6.4(1.0126)^{14} = 6.4*1.19160117479 = 7.62624751867$

Hence answer is approx 7.63 billion.

Answer(c):

Average rate of change of the world population between 2004 and 2018 is given by:

$\frac{P\left(Year_{2018}\right)-P\left(year_{2004}\right)}{2018-2004}$

$=\frac{P\left(14\right)-P\left(0\right)}{14-0}$

$=\frac{7.63-6.40}{14}$

$=0.0878571428571$

Hence answer is approx 0.0878571428571 billion per year.

To convert it into millions, multiply by 1000

So we get 0.0878571428571*1000 = 87.8571428571

Which is approx 88 to the nearest integer

Hence final answer is approx 88 millions per year.