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Modeling With Functions

Author: Shirley Beil

The following video will be available with closed captioning at:

http://youtu.be/ib5rQQ2H5hQ

A poster is 16 inches longer than it is wide. Find a function that models its area A in terms of its width w.

The following video will be available with closed captioning at:

http://youtu.be/txIfdPGN_pM

A rectangular box has a square base. Its height is one third the width of the base. Find a function that models its volume V in terms of its width w.

The following video will be available with closed captioning at:

http://youtu.be/9UpoIjYCeOY

A rectangle has a perimeter of 20 ft. Find a function that models its area A in terms of the length x of one of its sides.

The following video will be available with closed captioning at:

http://youtu.be/SeEMlu1Yw4c

A rectangle has an area of 19 m^2. Find a function that models its perimeter P in terms of the length x of one of its sides.

The following video will be available with closed captioning at:

http://youtu.be/nwnLT2t4IUY

Find a function that models the radius r of a circle in terms of its area A.

The following video will be available with closed captioning at:

http://youtu.be/p50dSHJBvHY

A rectangular box with a volume of 30 ft^3 has a square base. Find a function that models its surface area S in terms of the length x of one side of its base.

The following video will be available with closed captioning at:

http://youtu.be/tK3AvJkWsRA

Two ships leave port at the same time. One sails south at 15 mi/h, and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.

The following video will be available with closed captioning at:

http://youtu.be/rmnvRNCTbnE

The sum of two positive numbers is 70. Find a function that models their product P in terms of x, one of the numbers.

The following video will be available with closed captioning at:

http://youtu.be/m9sQvszfOiI

A right triangle has one leg four times as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

The following video will be available with closed captioning at:

http://youtu.be/jO4TTnfyvE4

Find two positive numbers whose sum is 196 and the sum of whose squares is a minimum. (Enter your answers as a comma-separated list.)

The following video will be available with closed captioning at:

http://youtu.be/Y9Hyjo1hZg0

An open box with a square base is to have a volume of 14 ft^3. Find the box dimensions that minimize the amount of material used

The following video will be available with closed captioning at:

http://youtu.be/WoSYpN2i1N0

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Modeling With Functions

A poster is 16 inches longer than it is wide. Find a function that models its area A in terms of its width w.

A rectangular box has a square base. Its height is one third the width of the base. Find a function that models its volume V in terms of its width w.

A rectangle has a perimeter of 20 ft. Find a function that models its area A in terms of the length x of one of its sides.

A rectangle has an area of 19 m^2. Find a function that models its perimeter P in terms of the length x of one of its sides.

Find a function that models the radius r of a circle in terms of its area A.

A rectangular box with a volume of 30 ft^3 has a square base. Find a function that models its surface area S in terms of the length x of one side of its base.

Two ships leave port at the same time. One sails south at 15 mi/h, and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.

The sum of two positive numbers is 70. Find a function that models their product P in terms of x, one of the numbers.

A right triangle has one leg four times as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

Find two positive numbers whose sum is 196 and the sum of whose squares is a minimum. (Enter your answers as a comma-separated list.)

An open box with a square base is to have a volume of 14 ft^3. Find the box dimensions that minimize the amount of material used

A rancher wants to build a rectangular pen with an area of 144 m^2. Find the pen dimensions that require the minimum amount of fencing.