14/14 14. Algebraic Modeling and Applications Free Online FlashCards

What are the main steps of algebraic modeling?

Define variables, organize information, write and solve the model, check the result, and interpret it in context.

Why must a model’s domain be checked?

A solution must satisfy the situation’s restrictions, such as nonnegative time, realistic dimensions, valid concentrations, and allowable integer counts.

What equation models uniform motion?

Use $D=rt$, where $D$ is distance, $r$ is rate, and $t$ is elapsed time.

How are combined work rates modeled?

Add completion rates, not completion times. A worker finishing in $a$ hours contributes $\frac{1}{a}$ job per hour.

What is the simple-interest formula?

Simple interest is $I=Prt$, where $r$ is the annual rate written as a decimal and $t$ is measured in years.

What formula models compound interest?

For interest compounded $n$ times per year, use $A=P\left(1+\frac{r}{n}\right)^{nt}$.

What are the rectangle area and perimeter formulas?

The rectangle’s area is $A=lw$, and its perimeter is $P=2l+2w$.

What is the constant-velocity position function?

A constant-velocity position model is $s(t)=s_0+vt$, where $s_0$ is initial position and $v$ is velocity.

What quadratic models vertical motion in U.S. customary units?

Near Earth, use $s(t)=-16t^2+v_0t+s_0$, with height in feet and time in seconds.

How is a quadratic optimum located?

For $f(x)=ax^2+bx+c$, the vertex occurs at $x=-\frac{b}{2a}$; it is a maximum when $a<0$.

How is ticket revenue modeled in the given example?

Revenue is price multiplied by quantity sold. In the ticket model, $R(x)=(20+2x)(120-10x)$.

Why is a negative geometry root rejected?

Reject a negative width because physical dimensions cannot be negative, even if the algebraic equation produces that root.