Question

The exponential model a = 69.5.0311 describes the population, a, of a country in millions, t years after 2003. Use the model to answer the following questions:

Answer 1

To find the population in the year 2100 using the logistic model, substitute the value of t as 2100 - 2003 = 97 into the equation. For the exponential result at 1% growth, calculate the population at 1% growth for the year 2100 using t = 2100 - 2003 = 97 in the equation.

Step-by-step explanation:

To find the population in the year 2100 using the logistic model, we need to substitute the value of t as 2100 - 2003 = 97 into the equation:
a = \frac{K}{1 + (\frac{K - P_0}{P_0}) \times e^{-r \times t}}
where K is the carrying capacity, r is the growth rate, and P_0 is the initial population.

Since the exponential model is given by a = 69.5 \times 1.0311^t, we can calculate the population at 1% growth for the year 2100 using t = 2100 - 2003 = 97 in the equation:
a = 69.5 \times 1.0311^{97}