### World Population Growth ModellingThe population of the world was recorded to be 5.28 billion in the year 1990 and 6.07 billion in the year 2000.#### Task Instructions:(a) **Finding an Exponential Model:** - Develop an exponential model to represent the population data given for the years 1990 and 2000. - Utilize the exponential model to predict the world population for the year 2020.(b) **Population Prediction:** - Based on your model, determine the year in which the world population is expected to exceed 10 billion.**Note:** An exponential model typically takes the form $ P(t) = P_0 e^{rt} $, where: - $ P(t) $ is the population at time $ t $, - $ P_0 $ is the initial population, - $ r $ is the growth rate, - $ t $ is the time in years, - $ e $ is the base of the natural logarithm.Apply this model to solve the tasks outlined above.

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The population of the world was 5.28 billion in 1990 and 6.07 billion in 2000. (a) Find an exponential model for these data and use the model to predict the world population in 2020. (b) According to your model, when will the world population exceed 10 billion?

The population of the world was 5.28 billion in 1990 and 6.07 billion in 2000. (a) Find an exponential model for these data and use the model to predict the world population in 2020. (b) According to your model, when will the world population exceed 10 billion?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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### World Population Growth Modelling

The population of the world was recorded to be 5.28 billion in the year 1990 and 6.07 billion in the year 2000.

#### Task Instructions:

(a) **Finding an Exponential Model:**
- Develop an exponential model to represent the population data given for the years 1990 and 2000.
- Utilize the exponential model to predict the world population for the year 2020.

(b) **Population Prediction:**
- Based on your model, determine the year in which the world population is expected to exceed 10 billion.

**Note:** An exponential model typically takes the form $ P(t) = P_0 e^{rt} $, where:
- $ P(t) $ is the population at time $ t $,
- $ P_0 $ is the initial population,
- $ r $ is the growth rate,
- $ t $ is the time in years,
- $ e $ is the base of the natural logarithm.

Apply this model to solve the tasks outlined above.

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