Expert Answers to Algebra 2 Problems

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. $f(t)=6(0.84{)}^t$

Without graphing, determine whether the function $y=0.3(1.25)x$ represents exponential growth or decay. State how you made the determination.

How do you tell which function—linear, exponential, or quadratic—best represents data?

The variable z is often used to denote a complex number and $\overline{z}$ is used to denote its conjugate. If $z=a+bi,$ simplify the expression
${\displaystyle z^2-{\bar{z}}^2}$

Show that an exponential model fits the data. Then write a recursive rule that models the data.
$\begin{array}{|ccccccc|}\hline n& 0& 1& 2& 3& 4& 5\\ f(n)& 162& 54& 18& 6& 2& \frac{2}{3}\\ \hline\end{array}$

Mr. Lopez picks up 2 pallets of dog food to deliver to the animal shelter. Each pallet contains 40 bags of dog food, and the dog food weighs $37\frac{1}{2}$ pounds per bag. What is the total weight, in tons, of the dog food Mr. Lopez delivers to the animal shelter?
A $1\frac{1}{2}$ T
B 2 T
C $2\frac{1}{2}$ T
D $\frac{3}{4}$ T

The following data was collected about students in Mr. Rexinger's high school statistics class. Wearing jeansNot wearing jeans Has long hair(below chin)77 Does not have long hair 513

1) Mr. Rexinger is playing a game with his students. He randomly chooses a mystery student from his class roster. If a player guesses the hair length of the mystery student correctly, the player gets an early-lunch pass. Madeline is the next player. To have the greatest chance of winning an early-lunch pass, should she guess that the student has long hair? Explain.

2) Mr. Rexinger tells Madeline that the mystery student is wearing jeans. Would you advise Madeline to change her guess? Explain.

3) In a previous course, you may have studied the association of two numerical variables by analyzing scatterplots and least squares regression lines. Associations between categorical events, like having long hair or wearing jeans, are determined by independence-if two events are independent, then they are not associated. Are the events $\{\text{not having long hair}\}$ and $\{\text{wearing jeans}\}$ associated for the students in Mr. Rexinger's class today? Explain the independence relationship using $P(A\text{given}B)=P(A)$.

4) Are the events $\{\text{not having long hair}\}$ and $\{\text{wearing jeans}\}$ mutually exclusive? Explain.

Identify each function as modeling either exponential growth or exponential decay. What percent of increase or decrease does the function model? ${\displaystyle y=0.1{\left(1.7\right)}^x}$

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: ${\displaystyle P\left(x\right)=a(x-\alpha )(x-\beta )(x-\gamma ),a\ne 0}$
Type 2: Two real zeros, one repeated: ${\displaystyle P\left(x\right)=a(x-\alpha )2(x-\beta ),a\ne 0}$
Type 3: One real zero repeated three times: ${\displaystyle P\left(x\right)=a(x-\alpha )3,a\ne 0}$
Type 4: One real and two imaginary zeros: ${\displaystyle P\left(x\right)=(x-\alpha )(ax2+bx+c),\Delta =b2-4ac<0,a\ne 0}$
Experiment with the graphs of Type 1 cubics. Clearly state the effect of changing both the size and sign of a. What is the geometrical significance of $\alpha ,\beta ,and\gamma ?\alpha ,\beta ,and\gamma$?

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.

$\begin{array}{}x& \text{g(x)}\\ \text{-1,-1}& \text{3}\\ \text{0}& \text{6}\\ \text{1}& \text{12}\\ \text{2}& \text{18}\\ \text{3}& \text{30}\end{array}$

One method of graphing rational functions that are reciprocals of polynomial functions is to sketch the polynomial function and then plot the reciprocals of the y-coordinates of key ordered pairs. Use this technique to sketch ${\displaystyle y=\frac{1}{f\left(x\right)}}$ for each function.

$a)f(x)=2x,$

b)f(x)=${\displaystyle 4x^2,}$,

$c)f\left(x\right)=x^2-1$

d) ${\displaystyle f\left(x\right)=x^3}$