Boost Your Math Modeling Skills

Write and solve an equation to determine the width w of the flag $[9.5ft]$
The length of an American flat is $1.9\times$ its width Equation $=9.5$
The width of the flag is feet.

${\displaystyle F=Gm1m\frac{2}{r^2}}$ for m2

The number of bags of mulch bb that a gardener needs to cover a garden depends on the area aa of the garden and the depth dd of mulch. Which of the following equations models the relationship between these variables?
A. b=kad
B. k=dab
C. d=kba
D. bda=k ​

Give an example of a context for a modeling problem where you are given that xy = 120 and you are minimizing the quantity 2x + 6y.

Global warming is a topic of concern and of political discussion. Without doing research, discuss how modeling might be used to determine what might be done to reduce global warming.

Colleen and Martin are modeling the data shown. Colleen thinks the model should be ${\displaystyle f\left(x\right)={5.754}^{x}3+2.912x^2-7.516x0.349}$. Martin thinks it should be ${\displaystyle f\left(x\right)=3.697x^2+11.734x-2.476}$. Is either of them correct? Explain your reasoning.
f(x) -2-190.5-2 -1511.5 00.4243

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay $1800 plus 3% of the assessed home value in taxes. The second bill requires taxes of $200 plus 8% of the assessed home value. What price range of home assessment would make the first bill a better deal?

Use the strategy for solving word problems modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

Chance (Fall 2004) published a study on modeling a certain pitch of a musical composition. Data on 147 famous compositions were used to model the number of times (y) a certain pitch occurs called entropy- as a straight-line function of year of birth (x) of the composer. On the basis of the scatterplot of the data, the standard deviation $\sigma \sigma$ of the model is estimated to be $s=.1$. For a given year (x), about 95% of the actual entropy values (y) will fall within d units of their predicted values. Find the value of d.

Give an example of a modeling problem where you are minimizing the cost of the material in a cylindrical can of volume 250 cubic centimeters.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is $10,000 and it costs $0.40 to produce each tape. The selling price is $2.00 per tape. How many tapes must be produced and sold each week for the company to generate a profit?

Isaac evaluates the function modeling Tony's grandparents house value, ${\displaystyle h\left(t\right)=10,000\cdot {\left(2\right)}^t}$, at t=2.5. The variable t represents the number of decades since 1960. What is h(2.5)?

Write an equivalent expression for 5(2x+y−3z) by modeling and by using the distributive property.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Marilda has a block of modeling clay that is 8 inches by 5 inches by 3 inches. She is experimenting with different shapes that can be made from the clay. Give your answers to the nearest tenth. What is the volume of the clay?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost $175. The mechanic charges $34 per hour. If you receive an estimate for at least $226 and at most $294 for fixing the car, what is the time interval that the mechanic will be working on the job?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 2800 pounds. If the elevator operator weighs 265 pounds and each cement bag weighs 65 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Reciprocal functions are useful for modeling situations where a constant amount is divided by one variable to produce the other variable. Make up a situation like this, then define the variables and write a reciprocal function that describes it.

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. [T] The Gompertz equation has been used to model tumor growth in the human body. Starting from one tumor cell on day 1 and assuming α=0.1α=0.1 and a carrying capacity of 10 million cells, how long does it take to reach “detection” stage at 5 million cells?

Evaluate f(x)⋅g(x) by modeling or by using the distributive property. f(x)=(−3x+2) and g(x)=(2x2−5x−1)