Honors Pre Calc - Section 1.10 Homework Flashcards

Vocabulary and formula flashcards covering word problems, modeling linear and quadratic functions, revenue optimization, and geometry constraints from Section 1.10 Homework.

Car rental weekly cost function

The linear function $f(x) = 0.02x + 25$ representing the weekly cost in dollars to rent a car with a fixed rate of $25$\text{ dollars} plus $0.02$\text{ dollars} per mile, where $x$ is the number of miles driven.

Mile run record function

The linear function $M(x) = 239.3 - 0.4x$ representing the record time in seconds for running a mile $x$ years after 1955, given an initial record of $239.3$\text{ seconds} decreasing by $0.4$\text{ seconds} per year.

Bus fare cost function without discount pass

The function $f(x) = 2x$ expressing the total monthly cost in dollars to use the bus without a discount pass, where $x$ is the number of times the bus is used in a month.

Bus fare cost function with discount pass

The function $g(x) = 0.5x + 30$ expressing the total monthly cost in dollars to use the bus with a $30$\text{ dollars} monthly discount pass that reduces each ride to $0.50$\text{ dollars}, where $x$ is the number of bus rides.

Bus discount pass breakeven point

The usage level of $20$ bus rides in a month at which the total monthly cost without a pass ($f(20) = 40$\text{ dollars}) equals the total monthly cost with a discount pass ($g(20) = 40$\text{ dollars}).

Stadium attendance function

The function $N(x) = -200x + 43400$ representing the number of spectators at a football game as a function of ticket price $x$, based on a baseline of $40000$ spectators at $17$\text{ dollars} per ticket decreasing by $200$ for each $1$\text{ dollar} price increase.

Stadium ticket revenue function

The function $R(x) = -200x^2 + 43400x$ representing the total revenue from a football game as a function of the ticket price $x$.

Airline passenger volume function

The function $N(x) = -50x + 16000$ representing the monthly passenger count on a route as a function of ticket price $x$, based on $6000$ passengers at $200$\text{ dollars} gaining $50$ passengers for each $1$\text{ dollar} decrease in ticket price.

Airline monthly revenue function

The function $R(x) = -50x^2 + 16000x$ representing the monthly route revenue as a function of ticket price $x$.

Lemon tree yield per tree function

The function $Y(x) = -7x + 980$ representing annual yield per tree in pounds when the tree density $x$ per acre exceeds $100$, accounting for a decrease of $7$\text{ pounds} per tree for each tree over $100$.

Lemon tree total acre yield function

The function $T(x) = -7x^2 + 980x$ expressing the total annual yield in pounds for an entire acre as a function of tree density $x$ when $x > 100$.

Running track enclosed area function

The function $A(r) = -\pi r^2 + 420r$ expressing the area enclosed by a track formed by a rectangle with semicircular ends, where the total track perimeter is $420$\text{ yards} and $r$ is the radius of the semicircles.

Shipping package volume function

The function $V(x) = 340x^2 - 4x^3$ representing the volume of a package with a square front of side length $x$ subject to a maximum length-plus-girth constraint of $4x + y = 340$\text{ inches}.