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Bradford Pear trees are commonly used in landscaping. Initially, it was believed they would be infertile, but they have cross-pollinated and are spreading. Suppose a county starts with 15,000 Bradford Pear trees, and they are increasing at a rate of 4% each year.

Additionally, this increase is resulting in the loss of Dogwood trees. Suppose the county started with 24,000 Dogwoods, but they are declining by 5% each year.

Write an exponential model for each tree population.

Answer :

Final answer:

To model exponential growth for Bradford Pear trees, use the formula P = P0 * (1 + r)^t. To model exponential decline for Dogwood trees, use the formula P = P0 * (1 + r)^t.

Explanation:

To create an exponential model for the population of Bradford Pear trees, we can start with the initial population of 15,000 and multiply it by 1 plus the growth rate of 4% (or 0.04) raised to the power of the number of years. The formula for exponential growth is: P = P0 * (1 + r)^t, where P is the population after t years, P0 is the initial population, r is the growth rate, and t is the number of years.

For the Dogwood tree population, we can use the same exponential growth formula, but with a negative growth rate of -5% (or -0.05) since the population is declining. The formula for exponential decline is: P = P0 * (1 + r)^t, where P is the population after t years, P0 is the initial population, r is the decline rate, and t is the number of years.

Learn more about Exponential Growth here:

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