Write a function, $h(t)$, to describe the plane's height over time, $t$,

Problem01- A 747 airliner has an initial climb rate of $1800$ feet per minute until it reaches a height of $10,000$ feet.

Luke and Logan play for the same baseball team. They practice at the Lions Park baseball field. Luke lives $3$ miles from the field, and Logan lives $2$ miles from the field.

a. First, plot a point to represent the location of the Lions Park baseball field.

b. Next, use your point that represents Lions Park, and draw a circle to represent all the possible places Luke could live.

c. Finally, use your point that represents Lions Park, and draw another circle to represent all the possible places Logan could live.

Describe the relationship between the two numbers.

Let's consider how to determine the number of minutes the plane has been flying (the input value) given a height in feet (the output value) using function notation.-

To determine the number of minutes it takes the plane to reach $7200$ feet using your function, substitute $7200$ for $h(t)$ and solve.

$$\begin{aligned} & h(t)=1800 t \\ & \begin{array}{l} \text { Substitute } \\ 7200 \text { for } h(t) . \end{array} \quad 7200=1800 t \\ & \frac{7200}{1800}=\frac{1800 t}{1800} \\ & 4=t \\ & \end{aligned}$$

After takeoff, it takes the plane $4$ minutes to reach a height of $7200$ feet.

Use your function to determine the time it will take the plane to reach each given height in feet. Write a complete sentence to interpret your solution in terms of the problem situation.

a. $5400$ feet

b. $9000$ feet

c. $3150$ feet

d. $4500$ feet

Solve each inequality and then graph the solution set on the number line. a) (-2.3)x>=7, b) 32>23-x, c) 2(x+6)<10

The plane has landed in the United Kingdom and the Foreign Language Club is ready for their adventure. Each student on the trip boarded the plane with $300 euro$. They each brought additional U.S. dollars with them to exchange as needed. The exchange rate from U.S. dollars to British pounds is $0.622101 euro$ pound to every dollar.

Identify the slope and interpret its meaning in terms of this problem situation.

In order to earn two $\$ 55$ gift cards, Alan's total sales, $f(b)$, needs to be at least $\$ 1100$. You can set up an inequality and solve it to determine the number of boxes Alan needs to sell.

$$\begin{array}{r} f(b) \geq 1100 \\ 3.75 b+25 \geq 1100 \end{array}$$

Solve the inequality in the same way you would solve an equation.

$$\begin{aligned} 3.75 b+25 & \geq 1100 \\ 3.75 b+25-25 & \geq 1100-25 \\ 3.75 b & \geq 1075 \\ \frac{3.75 b}{3.75} & \geq \frac{1075}{3.75} \\ b & \geq 286.66 \ldots \end{aligned}$$

Alan needs to sell at least 287 boxes of popcorn to earn two $\$ 55$ gift cards.

Write and solve an inequality for each. Show your work.

a. What is the greatest number of boxes Alan could sell and still not have enough to earn the Cyclone Sprayer?

b. At least how many boxes would Alan have to sell to be able to choose his own prize?

Were you able to complete the table using the TABLE feature? Why or why not? What adjustments, if any, can you make to complete the table?

A 747 airliner has an initial climb rate of $1800$ feet per minute until it reaches a height of $10,000$ feet.

2. Describe the units of measure for:

a. the independent quantity (the input values).

b. the dependent quantity (the output values).

GoodSportsBuys.com is an online store that offers discounts on sports equipment to high school athletes. When customers buy items from the site, they must pay the cost of the items as well as a shipping fee. At GoodSportsBuys.com, a shipping fee is added to each order based on the total cost of all the items purchased. This table provides the shipping fee categories for GoodSportsBuys.com.

What is the greatest amount a customer can spend on items and pay $\$ 6.50$ for shipping?

The official rules of baseball state that all baseballs used during professional games must be within a specified range of weights. The baseball manufacturer sets the target weight of the balls at $145.045$ grams on its machines. The specified weight allows for a difference of $3.295$ grams. This means the weight can be $3.295$ grams greater than or less than the target weight.

Suppose the manufactured baseball has a weight that is greater than the target weight.

a. Write an equation to represent the greatest acceptable difference in the weight of a baseball.

b. Solve your equation to determine the greatest acceptable weight of a baseball.

A 747 airliner has an initial climb rate of $1800$ feet per minute until it reaches a height of $10,000$ feet.

How do the first differences' and the rates of change between ordered pairs demonstrate that the situation represents a linear function? Explain your reasoning.

Describe the difference between a rate of change and a unit rate of change.

What do you notice about the rates of change?