2. Construct a mathematical model to predict the United States population starting in 1950. - Use a logistic population growth model \( \frac{d P}{d t}=r\left(1-\frac{P}{K} ight) P \), where P is the population, t is time, and r is a constant rate of growth or decline, K is the maximum capacity (estimated in part 1) - Solve for \( \mathrm{P}(\mathrm{t}) \) with \( r \) and the constant \( C \) are unknown. Hint: Convert it to either Bernoulli equation or use it as a separable equation. - Estimate the value for \( r \) using some data real points such as \( P(10)=176.19 \) (million) and \( P(20)=200.33 \) (million). Those are the as its U.S population in 1960 and 1970. You should use Desmos or Geogebra for this task, assume \( \mathrm{P}(0)=148.28 \) (million) (U.S population in 1950). Link to a Desmos template for this task: https://www.desmos.com/calculator/dqyc4pkuyz - Provide a graph of function \( \mathrm{P}(\mathrm{t}) \). You can screenshot a graph generated from the Desmos or Geogebra. - Compare function \( \mathrm{P}(\mathrm{t}) \) with the real data set. More specially, find \( \mathrm{P}(70) \) as the predicted U.S population using your model, and compare it with the real U.S