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Chapter 0: Problem 61
Rewrite each of the following as an equivalent expression using radical notation. $$y^{2 / 3}$$
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Jimmy decides to mow lawns to earn money. The initial cost of his lawnmower is 250 dollars. Gasoline and maintenance costs are 4 dollars per lawn. a) Formulate a function \(C(x)\) for the total cost of mowing \(x\) lawns. b) Jimmy determines that the total-profit function for the lawnmowing business is given by \(P(x)=9 x-250\) Find a function for the total revenue from mowing \(x\) lawns. How much does Jimmy charge per lawn? c) How many lawns must Jimmy mow before he begins making a profit?
Use the ZERO feature or the INTERSECT feature to approximate the zeros of each function to three decimal places. $$f(x)=|x+1|+|x-2|-3$$
The surface area of a person whose mass is 75 kg can be approximated by the function \(f(h)=0.144 h^{1 / 2}.\) where \(f(h)\) is measured in square meters and \(h\) is the person's height in centimeters. (Source: U.S. Oncology.) a) Find the approximate surface area of a person whose mass is 75 kg and whose height is 180cm. b) Find the approximate surface area of a person whose mass is 75 kg and whose height is 170cm. c) Graph the function \(f\) for \(0 \leq h \leq 200.\)
In general, people in our society are marrying at a later age. The median age, \(A(t),\) of women at first marriage can be approximated by the linear function \(A(t)=0.08 t+19.7\) where \(t\) is the number of years after \(1950 .\) Thus, \(A(0)\) is the median age of women at first marriage in 1950 \(A(50)\) is the median age in \(2000,\) and so on. a) Find \(A(0), A(1), A(10), A(30),\) and \(A(50)\) b) What was the median age of women at first marriage in \(2008 ?\) c) Graph \(A(t)\)
Suppose that \(\$ 5000\) is invested at \(8 \%\) interest, compounded semi annully, for \(t\) years. a) The amount \(A\) in the account is a function of time. Find an equation for this function. b) Determine the domain of the function in part (a).
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