Exam 7: Ingredients of Multivariable Change: Models, Graphs, Rates

The table below gives the value of an investment of P dollars after 2 years in an account whose annual percentage yield is 100r%. The value of a $10,000 investment after 2 years can be modeled by Find and interpret when the annual interest rate is 4.3%.

The per capita consumption of peaches can be modeled as where the price of peaches is and the person lives in a family with annual income $10,000i. Use this model to calculate the rate of change of the per capita consumption of peaches with respect to yearly income when the yearly income is $30,000 and the price is $1.70 per pound.

Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of Coke products, based on the prices of the products in the two machines are shown in the table below. Find an appropriate cross sectional model to estimate the sales of Coke products when the price of Coke is $1.50.

A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. Suppose that the percentage of the pigment that can be removed from a sunflower head by washing for 15 minutes can be modeled by percent where r milliliters of water is used for each gram of sunflower heads. Write a formula for the rate of change in the amount of water used with respect to a change in temperature when 47% of pigment is removed.

The face value of a loan is dollars where the payment amount of dollars is paid times a year for years at interest. Rewrite as a model with two input variables.

Consider the point on the contour graph of given below. When y is decreased by 2, by what amount must x change in order to remain on the same contour curve?

A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph and associated contour graph below show the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is Estimate how much water would be necessary to remove 37% of pigment removed from 4 grams of sunflower heads if the sunflower heads are washed for 25 minutes at

A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph and associated contour graph below show the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is Estimate the percentage of pigment removed from 20 grams of sunflower heads if the sunflower heads are washed for 5 minutes in 30 milliliters of water at

Consider the table of apparent temperatures (given below), which shows the apparent temperature (how hot it feels) given air temperature and dew point. In order to model apparent temperature as a function of the dew point when the air temperature is which variable must be held constant?

The figures show the profit (in hundred dollars) to craft fair organizers when hundred daily admission tickets and hundred weekend admission tickets to a large craft fair are purchased. Estimate the output value for point .

A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph below shows the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is Find and interpret the input and output values for the point A.

Draw the contour curves , and for the multivariable function for

Draw the contour curves and for the multivariable function for

If find .

The table shows the number of hours of daylight for a given month at a given latitude (measured in degrees away from the equator) for the northern and southern hemispheres. How many hours of daylight will there be at a location at latitude north in March?

The table shows per capita peach consumption. Find a cross-sectional model for a yearly income of $40,000.

Consider the graphs of below. At is decreasing when w decreases or when s decreases? Explain your answer.

The value of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function dollars. Write the partial derivative

Consider the table of apparent temperatures (given below), which shows the apparent temperature (how hot it feels) given air temperature and dew point. Consider a model of the apparent temperature as a function of the dew point when the air temperature is How is this information represented in the table?

If find .