In a Certain Country, the Rate of Increase of the Population

question 18

Multiple Choice

In a certain country, the rate of increase of the population is proportional to the population P(t) . In fact, $P ^ { \prime } ( t ) = 0.23 P ( t )$ Suppose that initially the country's population is 50,000, and that 10 years later there are 500,000 people. Which of the following equations expresses this information mathematically?

• A) 10 = \(e ^ { 2.3 t }\)
• B) 500 = \(e ^ { 2.3 ( 50 ) }\)
• C) 500,000 = \(\mathrm { e } ^ { 0.23 ( 10 ) }\)
• D) 500,000 = 50,000 \(e ^ { 2.3 }\)
• E) none of these

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