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\n(a) graph this function for ( 0leq lleq30 )\n(b) how many taxi miles are driven each day if there are 9 drivers employed?\n(c) does this model indicate that the number of taxi miles increases or decreases as the number of drivers increases?\n(d) is the graph of this function concave up or concave down? what does this mean?\n(a) choose the correct graph below.\n(b) if 9 drivers are employed, ( square ) miles are driven per day\n(round to the nearest integer as needed )

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\n(a) graph this function for ( 0leq lleq30 )\n(b) how many taxi miles are driven each day if there are 9 drivers employed?\n(c) does this model indicate that the number of taxi miles increases or decreases as the number of drivers increases?\n(d) is the graph of this function concave up or concave down? what does this mean?\n(a) choose the correct graph below.\n(b) if 9 drivers are employed, ( square ) miles are driven per day\n(round to the nearest integer as needed )

Answer

Explanation:

Step1: Substitute ( L = 9 ) into the function

Given ( Q = 338L^{0.2}), when ( L = 9), we have ( Q=338\times9^{0.2}). First, calculate (9^{0.2}). We know that (a^{b}=e^{b\ln a}), so (9^{0.2}=e^{0.2\ln9}). Since (\ln9=\ln(3^{2}) = 2\ln3\approx2\times1.0986 = 2.1972), then (0.2\ln9=0.2\times2.1972 = 0.43944), and (e^{0.43944}\approx1.5518).

Step2: Calculate the value of ( Q )

Now, (Q = 338\times1.5518). (Q=338\times1.5518 = 338\times(1 + 0.5+0.05 + 0.0018)=338+338\times0.5+338\times0.05+338\times0.0018) (=338 + 169+16.9+0.6084=524.5084\approx525)

Answer:

525