Population Growth Since 1960 , the growth in world...

Population Growth Since 1960 , the growth in world population (in millions) closely fits the exponential function defined by $A(t)=3100 e^{0.0166 t}$ where $t$ is the number of years since $1960 .$ Source: United Nations. (a) World population was about 3686 million in $1970 .$ How closely does the function approximate this value? (b) Use the function to approximate world population in $2000 .$ (The actual 2000 population was about 6115 million.) (c) Estimate world population in the year 2015 .

Population Growth Since 1960 , the growth in world population (in millions) closely fits the exponential function defined by
$A(t)=3100 e^{0.0166 t}$ where $t$ is the number of years since $1960 .$ Source: United Nations.
(a) World population was about 3686 million in $1970 .$ How closely does the function approximate this value?
(b) Use the function to approximate world population in $2000 .$ (The actual 2000 population was about 6115 million.)
(c) Estimate world population in the year 2015 .

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Key Concepts

Exponential Growth

Exponential growth describes processes where the rate of increase of a quantity is proportional to its current value. This concept is widely used in various fields, including population dynamics, where the population increases by a constant percentage over equal time intervals.

Exponential Function

An exponential function is a mathematical expression in which a constant base is raised to a variable exponent. In growth models, this function typically takes the form A(t) = A? e^(kt), where A? is the initial amount, k is the constant growth rate, and t represents time.

Model Accuracy and Approximation

When using an exponential model to predict actual values, assessing the accuracy of the function involves comparing the computed estimates with known data points. This comparison can reveal how well the model fits observed data, and it may guide adjustments or interpretations of its predictions.

Interpolation and Extrapolation

Interpolation involves estimating values within the range of observed data points using the model, whereas extrapolation involves predicting values outside of the observed data range. Both techniques are essential in applying mathematical models to forecast future trends or fill in gaps in existing data.

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