Suppose that the present population of a city is 150,000 ....

Suppose that the present population of a city is 150,000 . Use the equation $P(t)=150,000 e^{0.032 t}$ to estimate future growth. Estimate the population
(a) 10 years from now
(b) 20 years from now
(c) 30 years from now

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Key Concepts

Population Modeling

Population modeling uses mathematical functions to predict future population sizes based on current data and growth parameters. By using an equation like P(t) = P(0)e^(kt), one can estimate how a population evolves over time, assuming a constant proportional rate of growth.

Substitution into the Growth Equation

Substituting specific time values into the exponential growth equation is a standard method to calculate future or past values. This involves replacing t with the number of years into the equation, which allows for straightforward computation of the population at those particular times.

Exponential Growth

Exponential growth is a process where the rate of change of a quantity is proportional to the current amount of that quantity. In population dynamics, it implies that as the population increases, the growth rate also increases, leading to rapid growth over time when the growth constant is positive.

Natural Exponential Function

The natural exponential function, denoted as e^(kt), is central in modeling continuous growth processes. In this context, e^(0.032t) represents how the population multiplies over time, with 0.032 serving as the continuous growth rate.

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