the green hat taxi company estimated, on the basis of collected data, that the number of taxi miles driven…

the green hat taxi company estimated, on the basis of collected data, that the number of taxi miles driven each day can be modeled by the function ( q = 338l^{0.2} ), when they employ l drivers per day. (a) graph this function for ( 0 leq l leq 30 ). (b) how many taxi miles are driven each day if there are 9 drivers employed? (c) does this model indicate that the number of taxi miles increases or decreases as the number of drivers increases? (d) is the graph of this function concave up or concave down? what does this mean? (b) if 9 drivers are employed, 525 miles are driven per day (round to the nearest integer as needed.) (c) the number of miles driven per day increases as the number of drivers employed increases. (d) choose the correct answer below. a. the graph of the function is concave up. this means, that the graph of the function decreases at an increasing rate b. the graph of the function is concave up. this means, that the graph of the function decreases at an decreasing rate c. the graph of the function is concave down. this means, that the graph of the function increases at an decreasing rate. d. the graph of the function is concave down. this means, that the graph of the function increases at an increasing rate

the green hat taxi company estimated, on the basis of collected data, that the number of taxi miles driven each day can be modeled by the function ( q = 338l^{0.2} ), when they employ l drivers per day. (a) graph this function for ( 0 leq l leq 30 ). (b) how many taxi miles are driven each day if there are 9 drivers employed? (c) does this model indicate that the number of taxi miles increases or decreases as the number of drivers increases? (d) is the graph of this function concave up or concave down? what does this mean? (b) if 9 drivers are employed, 525 miles are driven per day (round to the nearest integer as needed.) (c) the number of miles driven per day increases as the number of drivers employed increases. (d) choose the correct answer below. a. the graph of the function is concave up. this means, that the graph of the function decreases at an increasing rate b. the graph of the function is concave up. this means, that the graph of the function decreases at an decreasing rate c. the graph of the function is concave down. this means, that the graph of the function increases at an decreasing rate. d. the graph of the function is concave down. this means, that the graph of the function increases at an increasing rate

Answer

Explanation:

Step1: Find the second - derivative of the function

Given (Q = 338L^{0.2}). First, find the first - derivative using the power rule ((x^n)^\prime=nx^{n - 1}). (Q^\prime=\frac{dQ}{dL}=338\times0.2L^{0.2 - 1}=67.6L^{- 0.8}) Then, find the second - derivative: (Q^{\prime\prime}=\frac{d^{2}Q}{dL^{2}}=67.6\times(-0.8)L^{-0.8 - 1}=-54.08L^{-1.8}=-\frac{54.08}{L^{1.8}}) Since (L>0) (number of drivers), (Q^{\prime\prime}<0)

Step2: Analyze concavity and its meaning

If (Q^{\prime\prime}<0), the function (Q = 338L^{0.2}) is concave down. For a function (y = f(x)) that is increasing ((f^\prime(x)>0)) and concave down ((f^{\prime\prime}(x)<0)), the rate of increase of the function is decreasing. Here, (Q^\prime=67.6L^{-0.8}>0) (because (L>0)) and (Q^{\prime\prime}<0). So the number of taxi miles (Q) increases as (L) increases ((Q^\prime>0)), but the rate at which (Q) increases is decreasing ((Q^{\prime\prime}<0))

Answer:

C. The graph of the function is concave down. This means, that the graph of the function increases at an decreasing rate.