Answer:
The model for the population P as a function of time t elapsed can be determined using the formula for exponential growth:
P(t) = P0 * e^(kt)
where P0 is the initial population, e is the mathematical constant approximately equal to 2.71828, k is the rate of growth, and t is the time elapsed.
We know that initially, the population consists of 150 individuals, so P0 = 150. After t = 45 years, the population consists of 1500 individuals. Substituting these values into the formula, we get:
1500 = 150 * e^(k*45)
Dividing both sides by 150, we get:
10 = e^(k*45)
Taking the natural logarithm of both sides, we get:
ln(10) = k*45
Dividing both sides by 45, we get:
k = ln(10)/45
Substituting this value of k into the formula, we get:
P(t) = 150 * e^((ln(10)/45)*t)
Therefore, the model for the population P as a function of time t elapsed is:
P(t) = 150 * e^((ln(10)/45)*t)