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in 1798, rev. robert malthus proposed that the rate of change of a population is proportional to the actual population at any given time. if the world population was 3.712 billion in 1970 and 4.453 billion in 1980, then what does malthus's law predict the world population to be in 2008?

User Xebeche
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Final answer:

Malthus's law can be used to predict the world population using the formula P(t) = P(0)e^kt. By calculating the growth rate using data from 1970 to 1980, we can find the predicted world population in 2008.

Step-by-step explanation:

Malthus's law states that the rate of change of a population is proportional to the actual population at any given time. To find the predicted world population in 2008, we can use the formula:

P(t) = P(0)e^kt

Where P(t) represents the population at time t, P(0) is the initial population, e is Euler's number (approximately 2.71828), k is the growth rate, and t is the time elapsed.

Given that the world population was 3.712 billion in 1970 and 4.453 billion in 1980, we can use these two data points to calculate the growth rate k:

4.453 = 3.712e^k(1980-1970)

Simplifying the equation, we have:

e^k = 4.453/3.712

k = ln(4.453/3.712)/(1980-1970)

Using the calculated growth rate, we can now find the population in 2008:

P(2008) = 3.712e^(k * (2008 - 1970))

User Joe Sewell
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