16. Suppose x and y grow at constant rates ğx and ğy, respectively. What is the growth rate of z if z = ? = a. gzagx + bğy b. 9z = (9x-9y) c. 9z = ağx bgy d. 9z ağxbgy
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- 1) Let the growth rate of X, be defined as the log difference a (X4) = log X – log X-1. For variables X, and Y, show that the growth rate of the quotient equals the difference of the growth rates, g g(Xt) – g (Y:).1.1. Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of its log to show: (a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) = X(t)Y(t), then Ż(t)/Z(t) = [X(t)/X(t)] + [Ÿ(t)/Y(t)]. (b) The growth rate of the ratio of two variables equals the difference of their growth rates. That is, if Z(t) = X(t)/Y(t), then Ż(t)/Z(t) = [X(t)/X(t)]-[Y(t)/Y(t)]. (c) If Z(t) = aX(t)a, then Ż(t)/Z(t) = aX(t)/X(t).10. The Reverend Thomas Malthus (a British economist) thought that arithmetic growth in food supply (such as a farmer adding five more bushels of apples to his harvest every year) exhibited: A. positive exponential growth (logarithmic increase) over time B. logistic growth (linear increase, then exponential, then linear again) over time C. saturation growth (Michaelis-Menten increases) over time D. negative exponential growth (logarithmic decrease) over time E. linear growth (straight line increase) over time
- Table 8 Amounts of New Solar Power Installed in the United States Amount of New Solar Power Installed Year (megawatts) 2006 2007 105 160 2008 290 2009 435 2010 878 2011 1891 3300 2012 Source: GTM Research If the model is given by: y 2.73(1.80)*, what is the growth rate? O the growth rate is 273%. O The growth rate is 80%. O can not be determined from the equation. O The growth rate is 73% O The growth rate is 180%. 99+ a1. Consider the variables x. V. and z. Assume that the growth rates of these variables aire given by g(x) = 0.04, g(y) = 0.12 and g(z) = 0.008. Then the growth rate of the variable w = %3D (yx)3/4(z)1/4 is approximately equal to a. 16% b. -10% с. 12% d. 12.5%Consider the trajectory showing the number of luggage pieces that an airline loses on aflight. What shape would a learning curve have in this setting?a. Exponential growthb. Exponential decayc. Diminishing return growth
- 12. The rule of 72 says that if something is growing by X% per period then it will double approximately every 72/X periods. The periods could be days, months, years, etc. In late February 2020 about 7,000 people outside of China had been infected with the COVID-19 virus and the number was increasing by 9% per day. If the growth rate stayed the same then how many times would be the number of infections double in the next 64 days? a. 8 times so about 56,000 people would be infected b. 1.125 times so about 15,000 people would be infected c. 1.125 times so about 8,000 people would be infected d. 8 times so about 1.8 million people would be infectedQuestion One. Answer the following pertaining to the growth theories. a) Derive the elasticity of the balanced-growth-path level of output with respect to savings rate. b) The Romer growth model assumed that growth rates if capital and knowledge are endogenously determined. Derive the growth rates of capital and knowledge. I want a answer in 15 minThe population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 10% in 10 years. What will be the population in 20 years? (Round your answer to the nearest person.) persons How fast (in persons/yr) is the population growing at t = 20? (Round your answer to two decimal places.) persons/yr
- Small differences in growth rates in the size of the economy, over several decades, will result in big differences in the size of the economy. Pretend we start in 1950 and the U.S. growth in real GDP has been around 3.15%. This has resulted in real GDP growing 8 times over this 70-year period (1950 to 2020). If real GDP growth had been 4.0%, real GDP would be times larger. a. 8 (about the same growth as with 3.15% growth) b. 10 С. 14 d. 16QUESTION 2 If Z = (XY)2, and we know that the annual growth rate of Z is 3%, and the annual growth rate of X is 2%, the annual growth rate of Y is а. - 1% b. - 0.5% C. 0.5% d. 1.0%An economist predicts that the cost of food will increase by 4% per year for the next several years. Part A: Use the economist's prediction to write an explicit rule for a geometric sequence that gives the cost in dollars of a box of cereal in year n that costs $3.20 in year 1. Part B: What is the fourth term of the sequence, and what does it represent in this situation? 5