Question

The population of a country dropped from million in 1995 to million in . Assume that p(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model. What is the population of the country in million in the year ?

Answer 1

The population of the country in the year t is P(t) million, and based on the given information, it can be determined using the exponential decay model that
`\( P(t) = P_0 \cdot e^(kt) \)`, where
`\( P_0 \)` is the initial population, k is the decay constant, and t is the time in years after 1995. To find the population in the year t, substitute the given values into the formula.

Step-by-step explanation:

The exponential decay model
`\( P(t) = P_0 \cdot e^(kt) \)` represents the population P(t) at any given time t years after 1995. In this case, the initial population
`(\( P_0 \))` is the population in 1995, and the problem states that the population dropped from
`\( P_0 \)` million in 1995 to P(t) million in the year t. The formula
`\( P(t) = P_0 \cdot e^(kt) \)` can be used to find P(t) by substituting the given values.

To solve for P(t), we substitute the known values into the formula. Let t represent the number of years after 1995. The initial population
`\( P_0 \)` is the population in 1995, and the final population P(t) is the population in the year t. The exponential decay formula becomes
`\( P(t) = P_0 \cdot e^(kt) \)`.

Next, the problem states that the population dropped from
`\( P_0 \)` million in 1995 to P(t) million in the year t. Therefore, to find P(t) in the given year t, substitute the values into the formula and solve for P(t).