Before the AIDS epidemic, Botswana had a rapidly growing population, as shown in the table below. In 2005, the population started decreasing.

Year 1975 1980 1985 1990

Population (millions) 0.755 0.90104 1.0753 1.2833

a) Show that the population growth between 1975 and 1990 is an exponential function (hint: prove that this data is exponential). Show all of your work and round decimals to three places.

b) Find an exponential model for the data. Let P(t) represent the population (in millions) as a function of the year, t, since 1975.

c) Use functional notation to express the population in the year 1995. Then show how you calculated the value. Round to four decimal places and include the correct unit of measure.

d) At the beginning of some year before1985, the population of Botswana surpassed 1 million people. Use your model from part (b) to determine which year. Explain how you found the solution. You can show your calculations or write a few sentences. Round to the nearest whole number. Answer in a complete sentence.