Assume that the population of the world in 2017 was 7.6 billion and is growing at the rate of 1.12% a year. a) set up a recurrence relation for the population of the links world n years after 2017. b) find an explicit formula for the population of the world n years after 2017. c) what will the population of the world be in 2050?

a)        

b)        

c)

Step-by-step explanation:

Given data:

Population in 2017 was 7.6 billion

r = 1.12%

a) population after n year 2017

It is given each year population rise at a rate of 1.12% Thus we have

b)

      ....

c)  for n = 33 year ( 2050- 2017 = 33 year)

Answered

Step-by-step explanation:

    r=    1.12%=   0.0112

a) let a_n represents population n years after 2017

each year population grows by 1.12 %. Thus the population is the population of the previous year multiplied by a factor of 1.12%.

that is

b) given

we successively apply the recurrence relation:

a_n= 1.0112a_n-1 = 1.0112^1a_n-1

.......................

=1.0112^na_n-n

=7.6×1.0112^n

c) the population of the world be in 2050

n=33 years

=7.6×1.0112^33

=10.975 billion

y=mx+b

step-by-step explanation:

m slope

b y-intercept