Final answer:
The increase in Mexico's population in the year 2025 can be calculated by taking the derivative of the given population model P(t) = 67e^(0.027t) with respect to time t and then evaluating it for the year 2025.
Step-by-step explanation:
The question involves determining how fast the population of Mexico is increasing in the year 2025, given a mathematical model. According to the population model P(t) = 67e0.027t, we need to calculate the rate of change of the population with respect to time, dP/dt, when t is the number of years after the initial time. In 2025, t equals the number of years since the starting point of the model. To find the rate of increase, we must take the derivative of P(t) with respect to t and then evaluate it at the year 2025.
First, find the derivative of P(t):
dP/dt = 67 * 0.027 * e0.027t.
Next, evaluate this at t corresponding to the year 2025:
dP/dt at t = 2025 is approximately the population change rate in millions of people per year.
The exact calculation will yield the increase rate for the year 2025, answering the student's question.