Math 151 HW 5D Directions: Use only the material through Section 3.2 for this home- work. No credit awarded for solutions that use material beyond Section 3.2. It is not necessary to use the definition of the derivative for any of these problems. Be sure to follow the Writing Requirements and Homework Checklist. In particular, see the Homework Checklist for the proper way to define a function. See the file Product Rule.pdf for more guidance on the specific type of problem that follows. Letter to a Friend: Problem 1 (5 points). The population of a small country was 4 million on January 1, 2022. At this same time the coun- try had a national debt of $8 billion. At this same moment, the population was decreasing at the rate of 120,000 people/year and the national debt was increasing at the rate of $320 milllion/year. (a) Determine the rate at which the per capita (ie. per person) share of the debt was changing at this moment. Be sure to provide a thorough expla- nation. Follow the solutions in the file ProductRule.pdf on our Homepage. In particular, show units for each number in every step of your computation. Do not assume that the above rates of change are constant. (b) Exlplain what is meant by a relative rate of change. Give a few of your own specific examples, with numbers. Then compute the relative rates of change in the population, national debt, and per capita share of the debt for the small country on January 1, 2022. (c) What do you notice about the relationship among the three relative rates of change in part (b)? Make a conjecture. Then choose different ab- solute growth rates for the population and national debt of the small country and see if your conjecture still holds. (d) What relationship between the relative growth rates in the population and national debt determines whether the per capita share of a country's national debt is increasing or decreasing? Try to prove your assertion