Final answer:
The exponential growth of the tamarix tree population introduced in 2006 is calculated using the exponential growth formula. With an initial population of 20 trees and a growth rate of 15%, the population is projected to reach 300 trees by the year 2024 (Option B).
Step-by-step explanation:
The question involves an exponential growth problem in which the tamarix tree population increases by a fixed percentage over time. To find the year when the population will reach 300, we must use the formula for exponential growth, P = P0ert, where P is the final population, P0 is the initial population, r is the growth rate, and t is time in years.
In this case, the initial population (P0) is 20 trees, the growth rate (r) is 15% or 0.15 when converted to decimal form, and the final population (P) we aim for is 300 trees. Solving for t gives us the number of years it takes to reach 300 trees, after which we add those years to the initial year, 2006, to get the year when the population reaches 300.
Upon solving the equation, we find that the population will reach 300 around the year 2024. Therefore, the correct answer is B) 2024.