Improve Your Math Modeling Skills with Practice Problems

An object moves in simple harmonic motion with period 8 minutes and amplitude 16 m. At time $t = 0$ minutes, its displacement d from rest is 0 m, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time f.

geduiwelh 2021-01-27

Marcus rowed 20 miles downstream in 2 hours. The trip back, however, took him 4 hours. Find the rate that Marcus rows in still water and the rate of the current. If x is Marcuss

jernplate8 2021-01-25

You just bought a new car for $22,000. Assume that the value of your new car depreciates at a constant $12 %$ per year.

1) The decay rate is square

2) The decay factor is square

3) The equation of the function that represents the value, V(t), of the car in dollars t years from now is $V = ◻$ (Write an expression that completes the function's equation.)

nicekikah 2021-01-22

The article “Modeling of Urban Area Stop-andGo Traffic Noise” presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table, were made at each location, in both the acceleration and deceleration lanes.
$\begin{array}{|c|c|}\hline \text{Location} & \text{Acceleration} & \text{Decelaration} \\ \hline 1 & 78.1 & 78.6 \\ \hline 2 & 78.1 & 80.0 \\ \hline 3 & 79.6 & 79.3 \\ \hline 4 & 81.0 & 79.1 \\ \hline 5 & 78.7 & 78.2 \\ \hline 6 & 78.1 & 78.0 \\ \hline 7 & 78.6 & 78.6 \\ \hline 8 & 78.5 & 78.8 \\ \hline 9 & 78.4 & 78.0 \\ \hline 10 & 79.6 & 78.4 \\ \hline \end{array}$
Can you conclude that there is a difference in the mean noise levels between acceleration and deceleration lanes?

ediculeN 2021-01-19

The population of a culture of bacteria is modeled by the logistic equation $P (t) = \frac{14, 250}{1 + 29 e - 0.62 t}$ To the nearest tenth, how many days will it take the culture to reach 75% of it’s carrying capacity? What is the carrying capacity? What are the virtues of logistic model?

CheemnCatelvew 2021-01-19

Determine the algebraic modeling The personnel costs in the city of Greenberg were $9,500,000 in 2009. In the recent past the personnel costs have increased at the rate of $4.2 %$ annually.
To model this, the city manager uses the function $C (t) = 9.5 {(1042)}^{t} where C (t)$ is the annual personnel costs,in millions of dollars, t years past 2009
1) Write the equation that can be solved to find in what year the personnel costs will be double the 2009 personnel costs.
2) Then solve the equation numerically (use the Table feature of your calculator) or graphically and determine the year.

floymdiT 2021-01-19

Define Logarithms? How Logarithms play an important role in modeling nonlinear regression functions?

Suman Cole 2021-01-17

Fill in the bla?

An equation that expresses a relationship between two or more variables, such as $H = \frac{9}{10} (20 - a)$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?

permaneceerc 2021-01-17

American automobiles produced in 2012 and classified as “large”; had a mean fuel economy of 19.6 miles per gallon with a standard deviation of 3.36 miles per gallon. A particular model on this list was rated at 23 miles per gallon, giving it a z-score of about 1.01. Which statement is true based on this information?

A) Because the standard deviation is small compared to the mean, a Normal model is appropriate and we can say that about $84.4 %$ of of large automobiles have a fuel economy of 23 miles per gallon or less.

Bergen 2021-01-16

Franco begins to save for a new Lego set that costs $65. His parents gave him $35 towards the cost and he plans to save $5 per week. Define all unknown variables. Write an equation modeling the total amount he has saved.

Suman Cole 2021-01-16

Consider that math modeling following initial valu problem
$\frac{d y}{d t} = 3 - 2 t - 0.5 y, y (0) = 1$
We would liketo find an approximation solution with the step size $h = 0.05$
What is the approximation of $y (0.1) ?$

rocedwrp 2021-01-05

The number of employees of a national company is given by $N (t) = 60 (1 .02)^{t} w h e r e N (t)$ is the number of employees in thousands,t years since 2005. What is the vertical intercept and what is the practical meaning of this intercept in this situation? A. (0,60), In 2005 there were 60 employees. B. (60,0), Initially there were 60 employees. C. (0,60), In 2005 there were 60,000 employees. D. (60,0), In 2005 there were 60,000 employees

Haven 2021-01-05

Make sure the provided power series is a solution to the given differential equation by directly substituting it. $[H i n t : For a power x^{2 n + 1} let k = n + 1.]$
$y = \sum_{(n = 0)}^{\infty} \frac{(- 1)}{2^{2 n} (n!)^{2}} x^{2 n}, x y^{n + y^{'}} = x y = 0$

illusiia 2021-01-04

Use your equation to determine the half-life ofthis type of lodine. That is, find out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs.

Wribreeminsl 2021-01-02

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time $t = 0$ , an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500 mg/L. The inflow rate is 0.06 L/min. Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant. a. Write an initial value problem that models the mass of the drug in the blood, for $t \geq 0$ . Solve the initial value problem, and graph both the mass of the drug and the concentration of the drug. c. What is the steady-state mass of the drug in the blood? d. After how many minutes does the drug mass reach 90% of its steady-state level?

foass77W 2020-12-30

Fully discuss whether we should omit a predictor from the modeling stage if it does not reflects any connection with the target variable in the EDA stage, and why.

Tabansi 2020-12-21

Use the property of exponents $a^{m} * a^{n} = a^{m + n}$ to determin the following product. $x^{4} y^{3}$
$x^{4} y^{3} =$ square

Nann 2020-12-16

Define the process of mathematical modelling?

UkusakazaL 2020-12-14

Illustrate and explain how you would introduce division of fractions by modeling $\frac{3}{4} - : \frac{1}{6}$ with Fraction Bars.

Joni Kenny 2020-12-13

Determine the algebraic modeling How much money will there be in an account at the end of 7 years if $2000 is deposited at $4 %$ interest compounded serni-annually?

Since Math modeling problems can be encountered anywhere from AI-based solutions to programming and design, questions that relate to this area of Algebra are always in demand. You can see various Math modeling examples below that provide help and solutions to various problems. While it may not address your particular challenge, taking a look at some solutions will always provide a great starting point. See several Math modeling questions first and compare them to see the rationality and the use of equations that make things easier.

Algebra II

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