Getting going in the morning was probably hard for folks on the Overland Trail (just as it may be for you today), so coffee was a highly valued commodity. The Cazneau family starts their journey with a supply of 30 pounds of coffee. When they arrive at Sutter's Fort in California, 188 days later, they have only 3 pounds left. 1. Draw a graph showing the amount of coffee remaining as a function of the time elapsed since the start of the journey. For simplicity, assume the Cazneaus consume coffee at a constant rate. 2. Find the average amount of coffee consumed per day. 3. Develop an equation for the function represented by your graph. 4. Find the slope of your graph. 5. Suppose that at the beginning of their 188-day journey, the Cazneaus are 1600 miles from Sutter's Fort. a. How many miles per day do they travel? For simplicity, assume they travel the same distance each day. b. Of course, as the Cazneaus travel, their distance from Sutter's Fort decreases. Write a formula expressing the distance remaining as a function of the number of days they have been traveling. grap of your function from part b.

1a. Make a scatter plot of the table provided in the image. B. Write a linear/exponential equation that models this table provided in the image. C. Explain what the slope/multiplier means in the context of the problem. E. Use your model to predict when there will be 100 new cases (I have already done question 1a and have included it in my images. I mainly need help with questions C, D, and E)

Write the equation of the line for each of the following situations. Recall that ? is the number of hours it has been snowing and ? is the number of inches of snow on the ground. 1) There are 6 inches of snow on the ground from a prior snowfall. Snow is now falling at a steady rate of 4 inches per hour. ? =

A local restaurant has a weekly fixed cost of $1507 per week, and unit costs of $1.75 per hamburger. They sell the hamburger for $5.99 a. Sketch the graph of the following cost and revenue functions. Shade and label the area of profit and loss

Despite booming new car sales with their​ cha-ching sounds, the average age of vehicles on roads is not going down. The bar graph shows the average price of new cars in Country A and the average age of cars on roads for two selected years. In 2014​, the average price of a new car was​ $37,600. For the period​ shown, new-car prices increased by approximately ​$1250 per year. If this trend​ continues, how many years after 2014 will the price of a new car average ​$43,850​? In which year will this​ occur?

2.  You bought a new computer for $2,500.  Four years later, your computer is valued at $1,250. a.  Assume that the cost function will be linear and write a linear function to describe the cost of the computer ?t years after you bought it. b.  Assume that the cost function will be exponential (think of exponential decay) and write an exponential function to describe the cost of the computer ?t years after you bought it. c.  For each function you just wrote, find the rate at which the cost is depreciating 3 years after you bought it. d.  Which function do you think would be more accurate?  Write a complete sentence or two describing why you think so.