In 1980 and 1996, the population of the US was 226.5 million and 266.0 million r
ID: 3124897 • Letter: I
Question
In 1980 and 1996, the population of the US was 226.5 million and 266.0 million respectively. Using this formula (see below) answer the following.
a. what was the average percentage increase per year
b. estimate the population in 1985
c. if the average percentage increase of population per year from 1996 to 2000 is the same as in part (a) what would the population be in 2000?
answers: a - 1.01% b- 238.2 million c- 276.9 million
formula A= P(1+R)^n
a= amount,p = some quantity, constant rate r per unit of time, n units of time
Please show all working and explain how the given answers were obtained. Thanks much.
Explanation / Answer
In 1980 the population of the US was 226.5 million and in 1996 it was 266.0 million.
a) so in (1996-1980)=16 years the population was increased by (266-226.5)=39.5 million from 226.5 million.
so in one year the increase was 39.5/16=2.46875 million from 226.5 million
so percentage increase was 2.46875*100/226.5=1.01
hence average percentage increase per year was 1.01% [answer]
b) we have to find the estimated population in 1985.
the formula is A= P(1+R)^n where a= amount,p = some quantity, constant rate r per unit of time, n units of time
so here P=226.5 A=estimated population in 1985 R=1.01%=0.0101 n=(1985-1980)=5
so A=226.5(1+0.0101)5=226.5*1.05153=238.2 million
hence the estimated population in 1985 is 238.2 million [answer]
c. if the average percentage increase of population per year from 1996 to 2000 is the same as in part (a)
then to calculate the estimated population in 2000 we have
A=estimated population in 2000 P=266 million n=(2000-1996)=4 R=1.01%=0.0101
so A=266(1+0.0101)4=266*1.041=276.90million
hence the estimated population in 1985 is 276.9 million [answer]