Boost Your Math Modeling Skills

An object moves in simple harmonic motion with period 5 seconds and amplitude 7 cm. At time ${\displaystyle t=0}$ seconds, its displacement d from rest is -7 cm, and initially it moves in a positive direction.
Give the equation modeling the displacement d as a function of time t.

c. Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both.

Use your equation to determine the half-life ofthis type of Fodine, 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

Discuss in brief infeasible solution?

Find the exponential function that models the data in the table below. $\overline{)\begin{array}{ccccccccc}x& -3& -2& -1& 0& 1& 2& 3& 4\\ y& 4/27& 4/9& 4/3& 4& 12& 36& 108& 324\end{array}}$ What is the exponential regression of the data? $y=square$ 

Tell whether the function represents exponential growth or exponential decay. Then graph the function.
${\displaystyle y=3e^{2x}}$

Discuss the data modeling concepts in DynamoDB.

Which of the following statements is/are correct about logistic regression? (There may be more than one correct answer) Logistic regression can be used for modeling the continuous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the dichotomous response variable with dichotomous explanatory variable Logistic regression can be used for modeling the continuous response variable with dichotomous or other type of categorical explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with dichotomous and not for continuous explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with categorical explanatory variables and/or continuous explanatory variables.

Modeling: Draw models to represents ${\displaystyle \frac{3}{4}}$ and ${\displaystyle 2\frac{3}{5}.}$

Create equations to represent a relationship between quantities.
Define appropriate quantities for $\cdots$ descriptive modeling.
Two trains leave a station heading in opposite directions. The first train travels at two-thirds the rate of the second train. If the trains are 360 miles apart after three hours, then at what rate (in mph) was each train traveling?

Answer true or false to each of the following statements and explain your answers. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.

Answer true or false to each of the following statements and explain your answers. Polynomial regression equations are useful for modeling more complex curvature in regression equations than can be handled by using the method of transformations.

Determine whether the statement makes sense or does not make sense, and explain your reasoning : By modeling attitudes of college freshmen from 1969 through 2013, I can make precise predictions about the attitudes of the freshman class of 2040.

Explain how simple regression modeling can be extended to understand the relationship among several variables?

Consider that algebraic modeling Identify the decay factor, if any, for each function. If there is no decay factor, type N.
1) ${\displaystyle y={0.8}^x}$
2) ${\displaystyle y=-3x-8}$
3) ${\displaystyle g\left(x\right)={\left(\frac{1}{2}\right)}^x}$

Determine the algebraic modeling a.
One type of Iodine disintegrates continuously at a constant rate of ${\displaystyle 8.6\mathrm{\%}}$ per day.
Suppose the original amount, ${\displaystyle P_0}$, is 10 grams, and let t be measured in days.
Because the Iodine is decaying continuously at a constant rate, we use the model ${\displaystyle P=P_0{e}^{k}t}$ for the decay equation, where k is the rate of continuous decay.
Using the given information, write the decay equation for this type of Iodine.
b.
Use your equation to determine the half-life ofthis type of Fodine, 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.

Give an example of a refinement in mathematical modeling with contextual explanation.

Which of the following statements is/are correct about logistic regression? Logistic regression can be used for modeling the continuous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the dichotomous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the continuous response variable with dichotomous or other type of categorical explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with dichotomous and not for continuous explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with categorical explanatory variables and/or continuous explanatory variables.

One type of lodine disintegrates continuously at a constant rate of 8.6% per day. Suppose the original amount, P0, is 10 grams, and let be measured in days. Because the lodine is decaying continuously at a constant rate, we use the model P = P0e for the decay equation, where k is the rate of continuous decay. Using the given information, write the decay equation for this type of lodine.

Define (i) mathematical modelling (ii) numerical modeling Identify the clss of equation (i) $2x+3=y,(ii)2x^3+2x+3=0$ (iii) $2sinx+sin{x}^2=1$