At the beginning of the year 1995, the population of Townsville was 3657. By the

Question

At the beginning of the year 1995, the population of Townsville was 3657. By the beginning of the year 2015, the population had reached 5198. Assume that the population is growing exponentially, answer the following A) Estimate the ROUND TO THE NEAREST PERSON. tion at the beginning of the year 2019 The population at the beginning of 2019 will be about B) How long (from the beginning of 1995) willit take for the population to reach 9000 ROUND TO 2 DECIMAL PLACES The population will reach 9000 about years after the beginning of 1995 C) In what year willdid the population reach 9000? The population will (or did) hit 9000 in the year

Explanation / Answer

a)

here t= 0 corresponds to year 1995,

hence t= 2015 -1995 = 20 corresponds to year 2015

Set up using A = Pe^(kt ) as

5198 = 3657*e^(20k)

k= ln(5198/3657) *1/20

k=0.01758154

Hence

A =3657e^(0.01758154t )

Substitute t= 2019 -1995 =24

A =3657e^(0.01758154*24 )

=5577 person

b)

3657e^(0.01758154t ) =9000

e^(0.01758154t ) =9000/3657

0.01758154t =ln(9000/3657)

t= ln(9000/3657) *1/0.01758154

t=51.22 years

c)

in year 1995 +51 =2046

it may accept 2047

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