Question

the population of a communitvs Known to incr ease at a rate proportional to the number of people present at time t. The initial population P has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years. What was the initial population P ? (Round your answer to one decimal place.) Po = _______

Answer 1

To find the initial population P, we can use the formula for exponential growth. Solving the system of equations, we find that the initial population is approximately 3,229.5.

Step-by-step explanation:

To solve this problem, we can use the formula for exponential growth. The formula is given by P(t) = P(0) * e^(kt), where P(0) is the initial population, t is time in years, k is the growth rate constant, and e is the base of the natural logarithm. We are given that the population doubled in 5 years, which means P(5) = 2P(0). We are also given that the population after 3 years is 9,000, so P(3) = 9,000. Using these two equations, we can solve for P(0) by setting up a system of equations and solving for P(0). After substituting the values and solving the system, we find that the initial population P(0) is approximately 3,229.5.

Learn more about exponential growth