5 Problems - SHOW ALL WORK!3. A cab company charges a $4 boarding rate in addition to its meter which is $ ¾ a dollar for every mile
A) What equation represents the rate of this company?
B) Graph the equation that represents the rate of this cab company?
4. The graph below represents the total number of smartphones that are shipped to a retail store over the course of 50 days.
Match each part of the graph (A,B,C) to its verbal description. Explain your reasoning behind your choice.
I. half of the factory workers went on strike, and not enough smartphones were produced for normal shipments.
II. The production schedule was normal, and smartphones were shipped to the retail store at a constant rate.
III. A defective electronic chip was found, and the factory had to shut down, so no smartphones were shipped.
5. The relationship between Jame’s account balance and time is modeled by the graph below:
a. Write a story that models the situation represented by the graph.
b. When is the function represented by the graph increasing? How does this relate to your story?
c. When is the function represented by the graph decreasing? How does this relate to your story?
3. A) The equation that represents the rate of this company is R(x) = 4 + (3/4)x, where R(x) represents the total cost in dollars and x represents the distance in miles.
B) To graph this equation, plot points on a coordinate plane where the x-axis represents the distance in miles and the y-axis represents the total cost in dollars. Start with the point (0,4) and then plot additional points based on the rate of $0.75 for every mile. Connect the points to form a line.
4. A) Part A of the graph (A) represents the situation where half of the factory workers went on strike, and not enough smartphones were produced for normal shipments. This is because the graph shows a decrease in the number of smartphones shipped.
B) Part B of the graph (B) represents the situation where the production schedule was normal, and smartphones were shipped to the retail store at a constant rate. This is because the graph shows a steady increase in the number of smartphones shipped.
C) Part C of the graph (C) represents the situation where a defective electronic chip was found, and the factory had to shut down, so no smartphones were shipped. This is because the graph shows a flat line with no increase or decrease.
5. a) The story that models the situation represented by the graph is as follows: "James opens a new bank account with an initial balance of $200. Over time, he deposits and withdraws money from his account. The graph shows the balance of his account over a period of time."
b) The function represented by the graph is increasing when the line is going upwards. This means that James is depositing more money into his account, leading to an increase in his balance over time. This relates to the story as it shows James adding money to his account.
c) The function represented by the graph is decreasing when the line is going downwards. This means that James is withdrawing money from his account, leading to a decrease in his balance over time. This relates to the story as it shows James taking money out of his account.