Solve each of the four problems below. Show all work!
Real-life Problems
1 The population of China was about 1.39 billion in the year 2013, with an annual growth rate of about 0.6%. This situation is represented by the growth function P(t) = 1.39(1.006)^t, where t is the number of years since 2013. To the nearest thousandth, what will the population of China be for the year 2031? How does this compare to the population prediction we made for India in Example 3? P. 468 in the text
2 A wolf population is growing exponentially. In 2011, 129 wolves were counted. By 2013, the population had reached 236 wolves. What two points can be used to derive an exponential equation modeling this situation? Write the equation representing the population N of wolves over time t.
3 An initial investment of $100,000 at 12% interest is compounded weekly (use 52 weeks in a year). What will the investment be worth in 30 years? (See the formula on p. 472 in our text)
4 Explain why the values of an increasing exponential functions will eventually overtake the values of an increasing linear function.
