QuestionJuly 15, 2025

A population numbers 19,000 organisms initially and grows by 19.4% each year. Suppose Prepresents population, and t the number of years of growth. An exponential model for the population can be written in the form P=acdot b^t where P=square

A population numbers 19,000 organisms initially and grows by 19.4% each year. Suppose Prepresents population, and t the number of years of growth. An exponential model for the population can be written in the form P=acdot b^t where P=square
A population numbers 19,000 organisms initially and grows by 19.4% each year. Suppose Prepresents population, and t the number of years of growth. An exponential model for the population can be written in the form P=acdot b^t where P=square

Solution
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Answer

P = 19000 \cdot 1.194^t Explanation 1. Identify Initial Population The initial population a is 19,000. 2. Determine Growth Rate The growth rate is 19.4\%, which means the population grows by a factor of 1 + \frac{19.4}{100} = 1.194 each year. 3. Write Exponential Model Substitute a = 19000 and b = 1.194 into the model P = a \cdot b^t.

Explanation

1. Identify Initial Population<br /> The initial population $a$ is 19,000.<br /><br />2. Determine Growth Rate<br /> The growth rate is $19.4\%$, which means the population grows by a factor of $1 + \frac{19.4}{100} = 1.194$ each year.<br /><br />3. Write Exponential Model<br /> Substitute $a = 19000$ and $b = 1.194$ into the model $P = a \cdot b^t$.
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