The population p, in millions, of a certain country can be calculated by p=0.83t54, where t is the time in years, and t = 0 represents the year 2015. find the expected population of this country in 2096. round your answer to the nearest whole million.

1. what must one do to perform the essential managerial task of controlling in achieving organizational goals? a. motivate, coordinate, and energize individuals and groups to work together to achieve organizational goals b. choose appropriate organizational goals and courses of action to best achieve those goals c. establish task and authority relationships that allow people to work together to achieve organizational goals d. establish accurate measuring and monitoring systems to evaluate how well the organization has achieved its goals

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?

Given the production function q=96(k^0.3)(l^0.7), find the mpk and mpl functions. is mpk a function of k alone, or of both k and l? what about mpl?