Exam 18: Growth and Form

You own a painting whose dimensions are 24 inches by 30 inches. If you create a postcard-sized reproduction of the painting whose area is 20 square inches, what is the scaling factor for the reproduction?

If points (0.4, 26) and (1.2, 41) lie on the graph of log y = B + a log x solve for a.

In 1997 a bottle of soda costs about 75 cents. Use the Consumer Price Index Table 21.5 to estimate when this soda would have cost 5 cents.

Artificial Christmas trees tend to be proportional in shape. If a 4-foot tree needs about two strings of lights, what size tree would need five strings of lights?

One of the famous problems of Greek antiquity was the duplication of the cube; that is, creating a cube similar to but double the volume of an existing cube. What if you instead wish to triplicate the cube, building a cube with three times the volume of an existing cube? What would be the scaling factor? Assuming the original cube was 1 cubic unit, what would be the dimensions of the larger cube?

The cost of photographic paper is nearly proportional to the area of the paper. You own a painting whose dimensions are 24 inches by 30 inches. You create a small photographic reproduction whose smaller side is 5 inches, and a large photographic reproduction whose smaller side is 8 inches. If the paper required for the small reproduction costs $1.50, how much will the paper required for the large reproduction cost?

Melissa's tractor-trailer gets 5 miles per gallon. About how much fuel does she use in traveling 1 kilometer?

A miniature model for a sculpture weighs about 10 ounces and stands 8 inches high. The actual model is to be 3 feet high and weigh about 25 pounds. Can it be made from the same material as the model? If not, how should its weight per cubic inch compare with that of the model material?

Other than the crushing strength considerations, what other factors limit the size of trees?

The weight of a block of granite 1 ft × 2 ft × 4 ft is 1320 lb. If 12 blocks are used to build a wall 8 ft high, 12 ft long, and 1 ft wide, what is the pressure on the bottom faces?

While vacationing, Mike buys a hat for 71 pesos in a shop in Mexico City. The exchange rate at the time of his visit is $1 U.S. = 9.48 pesos. What was the cost of the hat in U.S. dollars?

A granite sculpture weighs approximately 4500 lb. If a smaller version 2/3 the height of the original is created from granite, how much will it weigh?

You want to enlarge a sphere with 1-cm radius so as to double the ratio of surface area to volume. By what factor should you multiply the radius?

Karen's car gets 27 miles per gallon. What is this in liters per 100 kilometers?

A model of a truck is built to a scale of 1 to 54. If the model casts a shadow of 8 square inches, how large a shadow will the actual truck cast?

The cost of photographic paper is nearly proportional to the area of the paper. You own a painting whose dimensions are 24 inches by 30 inches. You create a small photographic reproduction whose smaller side is 5 inches. What is the scaling factor for this reproduction?

When comparing the relative dimensions of model trains you discover that their wheels are larger than they should be. Why might they be scaled incorrectly?

If log $a$ = 3, what is $\log ( 10 \cdot a ) ?$

How many square meters are in 2.1 square kilometers?

A sparrow has a minimum speed of about 20 miles per hour. If a blue jay is five times as long as a sparrow and proportional in shape, what is the minimum speed of a blue jay?