Questions: The Speedy Max 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(L) = 435L^0.5, when they employ L drivers per day. (a) How many taxi miles are driven each day if there are 12 drivers employed? (b) Graph the function.

The Speedy Max 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(L) = 435L^0.5, when they employ L drivers per day.
(a) How many taxi miles are driven each day if there are 12 drivers employed?
(b) Graph the function.

Transcript text: The Speedy Max Taxi Company estimated, on the basis of collected data, that the number of taxi miles driven each day can be modeled by the function $Q(L)=435 L^{0.5}$, when they employ $L$ drivers per day. (a) How many taxi miles are driven each day if there are 12 drivers employed? (b) Graph the function.

Solution

Solution Steps

Step 1: Calculate Taxi Miles for 12 Drivers

To find the number of taxi miles driven each day with 12 drivers, we use the function $ Q(L) = 435 L^{0.5} $.

Substitute $ L = 12 $:

\[ Q(12) = 435 \times 12^{0.5} \]

Calculate $ 12^{0.5} $:

\[ 12^{0.5} \approx 3.4641 \]

Now calculate $ Q(12) $:

\[ Q(12) = 435 \times 3.4641 \approx 1507.384 \]

Final Answer

The number of taxi miles driven each day with 12 drivers is approximately 1507.384 miles.

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