In 2020, the population of Australia was 25 million and was growing at 1.36%/year, while the population of the United States was 330 million and was growing at 0.71%/year. Assume that both countries' populations keep growing at these per capita rates. (a) Let A(t) and U(t) be the populations of Australia and the United States, re- spectively. Write down the rate equations that govern the growth of these functions. (b) What were the net growth rates A (2020) and U (2020) in 2020? (c) In general, does a country with a higher per capita growth rate necessarily have a higher net growth rate? (d) On average, how many seconds did it take for the population of Australia to increase by 1 in 2020? For the population of the United States? (A year is about 31.6 million seconds.)