Question

The exponential function describes the population of a city t years after 2000. What is the population in the year 2000?

Answer 1

To determine the population of the city in the year 2000 using an exponential function, we generally need to look at the function itself. An exponential function for population is typically expressed in the form:

\[ P(t) = P_0 e^{kt} \]

where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population (the population at \( t = 0 \), which corresponds to the year 2000),
- \( k \) is a growth rate constant,
- \( e \) is the base of the natural logarithm,
- \( t \) is the number of years since 2000.

In this context, to find the population in the year 2000 (which corresponds to \( t = 0 \)), you simply evaluate the function at \( t = 0 \):

\[ P(0) = P_0 e^{k \cdot 0} = P_0 e^0 = P_0 \]

Thus, the population in the year 2000 is equal to \( P_0 \).

Without having the specific values from the exponential function given in your question, I cannot provide an exact number for the population in the year 2000. However, \( P_0 \) represents that value. If you have the equation or values for the function, please share that information for a more precise answer.