Questions: The exponential model A=231.9 e^(0.004 t) describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.

The exponential model A=231.9 e^(0.004 t) describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.
Transcript text: The exponential model $\mathrm{A}=231.9 e^{0.004 t}$ describes the population, A , of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was $\square$ million.
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Solution

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Solution Steps

Step 1: Determining Population in the Future

To predict the population \(A\) in a future year, we use the formula \(A = P e^{rt}\), where:

  • \(P = 231.9\) million is the initial population in the base year (2003).
  • \(r = 0.004\) is the rate of growth (or decay).
  • \(t = 0\) years after the base year (2003).

Substituting the given values into the formula, we get: \(A = 231.9 \cdot e^{0.004 \cdot 0}\) = 231.9 million.

Final Answer:

The predicted population in the year 2003 is approximately 231.9 million.

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