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Chapter 11: Problem 61
Find a function \(f\) that satisfies the conditions. $$ f^{\prime \prime}(x)=x^{-2 / 3}, \quad f^{\prime}(8)=6, \quad f(0)=0 $$
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Two models, \(R_{1}\) and \(R_{2}\), are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with \(t=7\) corresponding to \(2007 .\) Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period? $$ R_{1}=7.21+0.58 t, R_{2}=7.21+0.45 t $$
You are given the rate of investment \(d l / d t\). Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation \(=\int_{0}^{5} \frac{d l}{d t} d t\) where \(t\) is the time in years. $$ \frac{d I}{d t}=500 $$
Use the Midpoint Rule with \(n=4\) to approximate the area of the region bounded by the graph of \(f\) and the \(x\) -axis over the interval. Compare your result with the exact area. Sketch the region. $$ f(x)=4-x^{2} $$ $$ [0,2] $$
Find the amount of an annuity with income function \(c(t)\), interest rate \(r\), and term \(T\). $$ c(t)=\$ 2000, \quad r=3 \%, \quad T=15 \text { years } $$
Two models, \(R_{1}\) and \(R_{2}\), are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with \(t=7\) corresponding to \(2007 .\) Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period? $$ R_{1}=7.21+0.26 t+0.02 t^{2}, R_{2}=7.21+0.1 t+0.01 t^{2} $$
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