Question

The population of a town increases every year by 2% of the population at the beginning of
that year. The number of years by which the total increase of population be 40% is
(a) 7 years
(b) 10 years
(c) 17 years (app) (d) none of these​

Answer 1

Answer:

that means after 17 years the total increase in the population will be 40% of that of initial population.

Explanation:

Lets assume that the initial population was P

now after a year population will be

= P+(2/100)P

=P(102/100)

=1.02P

Similarly after 2 years population will be

=1.02x1.02xP

So after n number of years population will be

=P x (1.02^n)

now this population should be equal to P+40%P, so

1.4P=P x (1.02^n)

1.4=1.02^n

1.02^17=1.02^n

so n=17

that means after 17 years the total increase in the population will be 40% of that of initial population.

Answer 2

Answer:

(c) 17

Explanation:

Lets assume that the initial population was P

now after a year population will be

= P+(2/100)P

=P(102/100)

=1.02P

Similarly after 2 years population will be

=1.02x1.02xP

So after n number of years population will be

=P x (1.02^n)

now this population should be equal to P+40%P, so

1.4P=P x (1.02^n)

1.4=1.02^n

1.02^17=1.02^n

so n=17

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