Answer Happy

Solve the following questions. Show all the steps involved in your solution. Please follow the solution format discussed in "Syllabus Overview". 1) (5 pt) World population in 1850 has been estimated at about 1 billion. World population reached 4 billion in 1975. Assuming the exponential growth with continuous compounding, estimate the rate of growth that would produce those numbers. Assume the growth rate was constant during that period. 2) (10 pt) Tuition at a major university rose from $1,500/yr in 1962 to $20,000/yr in 1995. (a) (5 pt) What exponential rate of growth (continuous compounding) characterized that period? Assume the growth rate was constant during that period. (b) (5 pt) If that growth rate were to continue for another 25 years (enough time for current students to have children in college!), what would the tuition be? 3) (15 pt) Over a 10,000-year period, the world's population increased from about 5 million to 1 billion in 1850. (a) (5 pt) If assumed constant, what was the exponential rate of growth (continuous compounding) during that period? (b) (5 pt) Had that rate continued, what would the population have been in the year 2000? (c) (5 pt) What was the actual world population in the year 2000 (Hint: Google it)? Compare it with the answer from part (b) and discuss the difference(s), if any. 4) (10 pt) Suppose human population grows from 6.3 billion in 2000 to an ultimate population of 10.3 billion following a logistic curve. Assuming a growth rate of 1.5 percent in 2000, when would the population reach 9 billion?