Exponential model for population. Assume that Switzerland's population grows at a rate of 0.18 percent a year and that the 1988 population was 6.7 million.

Nola Aguilar

Nola Aguilar

Answered question

2022-11-09

Exponential model for population
I am having trouble with a population modeling problem. The first part states:
Assume that Switzerland's population grows at a rate of 0.18 percent a year and that the 1988 population was 6.7 million.
I got the model to be:
y ( t ) = ( 6.7 × 10 6 ) e 0.0018 t
I am having trouble with the second part of the problem:
If there is a net immigration of 10,000 people a year into Switzerland, write an expression for the population in year t.
I have tried multiple variations of adding 10000 and 10000t to different parts of the equation with no luck.
How do I account for the 10000 immigrants?

Answer & Explanation

tiulowyn9v

tiulowyn9v

Beginner2022-11-10Added 7 answers

Step 1
Suppose population grow of a country is with a rate k and a constant immigration I in a year, so the population P(t) satisfies in differential equation
d P d t = k P ( t ) + I
Step 2
where t (uasally) in year and P(0) is initial population in first year. We solve this equation, then
P ( t ) = P ( 0 ) e k t + I k e k t I k

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