In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014.

Question

Douglas Spears

Mathematics

27 June, 00:49

In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014.

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Paxton Cobb · Answer 1

P = 1.236 * (1.0125) ^t

Step-by-step explanation:

As the Population increases at a rate proportional to itself, this is an exponencial growth, so we can write the following formula:

P = Po * (1+r) ^t

where P is the population after t years, Po is the inicial population (at t=0), r is the rate of growth and t is the amount of time in years.

For our problem, we have that Po = 1.236 and r = 0.0125.

Finally, we can write the equation for P:

P = 1.236 * (1.0125) ^t