The table below shows the length and weight of a species of fish.

Fish Lengths and Weights

Length (in.)	8	11	15	19	27	36

| Weight (lb) | $1.63$ | $2.52$ | $4.18$ | $6.58$ | $19.95$ | $62.86$

A commercial fishing boat catches fish of this species with an average length of 24 inches. If the total weight of their catch one day was $3.1$ tons, how many fish did they catch?

Given $f(t)=f_1(t) f_2(t)$, show that $F(\omega)=$ $(1 / 2 \pi) \int_{-\infty}^{\infty} F_1(u) F_2(\omega-u) d u$. Hint: First, use the defining integral to express $F(\omega)$ as

$$F(\omega)=\int_{-\infty}^{\infty} f_1(t) f_2(t) e^{-j \omega t} d t .$$

Second, use the inversion integral to write

$$f_1(t)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} F_1(u) e^{j \omega t} d u .$$

Third, substitute the expression for $f_1(t)$ into the defining integral and then interchange the order of integration.

For many species of fish, the weight W is a function of the length x, given by $W=k x^3$, where k is a constant depending on the species. Suppose k=0.002, W is in pounds, and x is in inches, so the weight is $W(x)=0.002 x^3$.

a. Find the inverse function of this function.

b. What does the inverse function give?

c. Use the inverse function to find the length of a fish that weighs 2 pounds.

d. In the context of the application, what are the domain and range of the inverse function?

The table below shows the length and weight of a species of fish.

Fish Lengths and Weights

| Weight (lb) | $1.63$ | $2.52$ | $4.18$ | $6.58$ | $19.95$ | $62.86$

A study found that only fish older than 5 years of age should be harvested for the fish population to recover. The equation $y=5.2 x+3.8$ models the length of the fish based on age, where $x$ is age in years and $y$ is the length in inches. Make a judgment based on this model and your model from part (a) to decide how a fisherman can use weight to determine whether a fish is old enough to be harvested.

A sample of a mixture containing only sodium chloride and potassium chloride has a mass of 4.000 g. When this sample is dissolved in water and excess silver nitrate is added, a white solid (silver chloride) forms. After filtration and drying, the solid silver chloride has the mass 8.5904 g. Calculate the mass percent of each mixture component.

The table below shows the length and weight of a species of fish.

Fish Lengths and Weights

| Weight (lb) | $1.63$ | $2.52$ | $4.18$ | $6.58$ | $19.95$ | $62.86$

Find an exponential model for the data.

Use your graphing calculator to write a quadratic function for the given set of data.

Find a quadratic model for the data in the table.

Read the question given below. Then write the letter of the correct answer on your paper.

A sixth-degree polynomial equation with rational coefficients has roots $-1,2 i$, and $1-\sqrt{5}$. Which of the following cannot also be a root of the polynomial?

I. 1

II. $-2 i$

III. $\sqrt{5}$

IV. $1-i$

A. I only

B. II and III only

C. III and IV only

D. II, III, and IV only

Which type of function best models the data in each table? Write an equation to model the data.

Read the question given below. Then write the letter of the correct answer on your paper.

Which best describes the transformations used to obtain the graph of $y=3(-x+3)^3$ from the graph of $y=x^3$?

F. reflect across the $x$-axis, shift left 3 units, stretch by a factor of 3

G. reflect across the $y$-axis, shift right 3 units, stretch by a factor of 3

H. reflect across the $x$-axis, shift right 3 units, stretch by a factor of 3

J. reflect across the $y$-axis, shift left 3 units, stretch by a factor of 3

Which type of function best models the data in each table? Use differences or ratios to find the type of function.

Use your graphing calculator to write an exponential function for the given set of data.

Use a graphing calculator to answer the exercise given below.

For the function $y=3.68 x-9.61$, what is $f(1.3)+f(5.2)$?