The fare of $(20 - 2.5) = $17.5 will maximize the total fare.
<h3>What is Differentiation?</h3>
Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.
Here, The operator for a round-trip fare of $20, carries an average of 500 people per day.
It is estimated that 20 fewer people will take the trip, for each $1 increase in fare.
for $x increase in fare, 20x less people will take the trip and at that time the total fare F is given by
f(x) =(20 + x)(500 - 20x)
f (x) = 10000 + 100x - 20x²
For f(x) to be maximum, the condition is dy/dx = 0
100 - 40x = 0
⇒ x = 2.5
Thus, the fare of $(20 - 2.5) = $17.5 will maximize the total fare.
Learn more about Differentiation from:
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Set up an equation to solve.
$8.50x (since it is the rate of change) + $12 (flat fee) = total money earned (or y). In this case, we have the total, amount, and are looking for x. Plug $139.50 into the equation.
$8.50x + $12 = $139.50
Now, solve for x.
$8.50x + $12-12 = $139.50-12 > <em>$8.50x = $127.5</em>
$8.50/8.50x = $127.5/8.50 > <em>x = 15</em>
So, the correct answer is <u>D. Olivia babysat for 15 hours.</u>
23, 710, 23, 751, 23, 715 Least to greatest
23, 23, 23, 710, 715, 751
