The area of an egg's shell is directly proportional to the 2/3 power of the mass of the egg. Suppose that a normal 60 gram chicken egg has a shell area of 28 square centimeters.
Let x = number of grams
Let y = number of square centimeters. 1. State the general equation.
2. Find the particular equation.
2 3
c = 1.8269m
3. Find the surface area of a 1600 gram ostrich egg. Round to the nearest cm2
250 cm2
4. Suppose that a lizard's egg has a surface are of 0.6 square centimeters. Find the mass. Round to the nearest hundredth.
.19 gm
5. Does doubling the mass cause the surface area to double?
no!
A rule of thumb used by chemical engineers to estimate the cost of a chemical factory is that the cost is directly proportional to the 0.6 power of the amount of chemical the factory produces per unit time. Suppose that a toothpaste factory, which turns out 15 tons per day of tooth paste, costs $43 million to build. a. Write the particular equation expression the cost of a toothpaste factory in terms of the number of tons per day it produces. b. Predict the cost of building a factory to produce,
1. 500 tons per day
2. 0.07 tons per day
c. If you double the manufacturing capacity of a toothpaste factory will the cost be double, more than double or less than double? Justify your answer. not a linear relationship, so not double. Using the multiply­multiply property.
2. Based on info in the July 1975 issue of Scientific America, the frequency with which a tree branch sways is inversely proportional to the square root of the branch's length.
a. A red maple branch 200 centimeters long sways with a frequency of about 140 cycles per minute when it is without leaves. Write the particular equation expressing frequency in terms of length.
b. When the same branch has leaves, it sways with a frequency of about 66 cycles per minute. Write the particular equation for red maple branches with leaves. c. Suppose that you observe a red maple branch (with leaves) too high off the ground to measure its length. However, you find that it sways with a period of 40 cycles per minute. About how long is this branch?
3. The number of minutes it takes to cook bacon in a microwave oven depends on how many slices you put in at once. A popular brand of oven specifies 1.75 minutes for 2 slices and 2.5 minutes for 4 slices. a. Explain why the number of minutes does not vary directly with the number of slices. b. Assume that the number of minutes varies directly with some power of the number of slices (not necessarily an integer power). Use the two given ordered pairs to derive the particular equation expression the number of minutes in terms of the number of slices. c. Where would you set the timer to cook 8 slices? 6 slices? 1 slices? d. The timer on the oven can be set for as much as 30 minutes. What is the maximum number of slices that could be cooked at once?
e. What are the domain and range of the function? f. What things in the real world would make the domain even smaller than the domain you wrote in part e?