Exam 18: Growth and Form

Artificial Christmas trees tend to be proportional in shape. If a 4-foot tree needs approximately 60 ornaments to cover the outer limbs of the tree, how many ornaments will a 6-foot tree need?

When a bird doubles its weight, how much do its wings grow?

Are all pentagons similar? Why or why not?

In 1965 powdered gelatin cost 10 cents per box at the grocery store. If the 1965 CPI is 31.5 and the 1999 CPI is 166.2, compute this cost in 1999 dollars.

Assuming that the sail of the Dimetrodon developed to dissipate heat when an individual doubled in weight, how much did the sail grow?

In 1976 a roast beef sandwich cost 89 cents at a local fast food shop. If the 1976 CPI is 56.9 and the 1999 CPI is 166.2, compute this cost in 1999 dollars.

A spherical balloon has a circumference of 10 inches. If it expands to twice the volume, what happens to its circumference?

Create an example of an advertisement that misuses proportional change through its use of graphics.

You own a painting whose dimensions are 24 inches by 30 inches. If you create a slide of this work so that the longest side of the image is 1 inch, what is the scaling factor for the slide?

A dog food company sells food in cans of two sizes. A "petite" can is 4 inches tall and a "super" can is 1 foot tall. The two types of cans are geometrically similar in shape. It costs the company 55 cents to produce the dog food in the super can. How much does it cost to produce the dog food in the petite can?

Christmas trees tend to be proportional in shape. You have a tree skirt that is circular and with diameter 3 feet, which you bought for a 7-foot tree. If you have a 5-foot tree this year, what size tree skirt will you need? (Round to the nearest size.)

The weight of a block of granite 1 ft × 2 ft × 4 ft is 1320 lb. If it stands on a large face (4 ft × 2 ft), what is the pressure on the bottom face?

A 100-hectare plot of land is about:

Each year, the area's largest tomatoes and pumpkins are showcased at the county fair. If there is a maximum size for such produce, how can larger and larger specimens be grown each year?

Find the values of a and b so that the points (1.1, 14) and (1.4, 38) lie on the curve y = bx^a.

Hisashi has a radio-controlled plane that is a scale model of a Boeing 727. The model has a 2-foot wingspan, and the wingspan of a Boeing 727 is 108 feet. If the minimum flight speed for a Boeing 727 is about 165 miles per hour, what is the minimum flight speed for the model plane?

Suppose that a quantity S is proportional to the surface area of an object. If another quantity M is proportional to the volume of the object, then for what power of M is the quantity S proportional to?

Melissa's tractor-trailer gets 5 miles per gallon. Approximately what is this in liters per 100 kilometers?

If points (1,32) and (3,75) lie on the graph of log y = bx^a, solve for a.

Are all rectangles similar? Why or why not?