23. Population Growth The population of the United States is expected to grow from 282 million in 2000 to 335 million in 2020.

a. Find a function of the form P(t) = Ce^kt that models the population growth of the United States. Here, t is the number of years since 2000, and P(t) is in millions.

b. Assuming the trend in part (a) continues, in what year will the population of United States be 350 million?

25. Housing Prices The median price of a home in the United States rose from $175,000 in 2000 to $280,000 in 2007.

a. Find an exponential function P(t) = Ce^kt that models the growth of housing prices, where t is the number of years since 2000.

b. The median price of a home in the U.S. dropped to $180,000 in 2012. Why is the model in part(a) inadequate for predicting the price in 2012?

27. Wildlife Conservation The population of white-tailed deer in a wildlife refuge t months after their introduction into the refuge can be modeled by the logistic function

N(t) = 300/(1+14e^-0.05t)

a. How many deer were initially introduced into the refuge?

b. How many deer will be in the wildlife refuge 10 months after introduction?

38. Explain why the function f (t) = e ^(1/2t) cannot model exponential decay.