Math 141 Take home quiz 1. Name _________________________________________

1. Linear Depreciation: A new car sold for $30000 in 2004. It depreciated linearly so that its value in 2008 was $20200.

a) Find the value of the car as a function of its age in years, t.

b) What will be the value of the car in 2011?

2. Break Even Point: A small manufacturer estimates his rent, machinery and other fixed costs total $2720. Each unit costs an additional $10 to produce and sells for $15.

a) Find the cost, revenue and profit functions with x=quantity produced.

b) Graph the three functions labeling the break even point and the x-intercept of the profit function.

3. Supply and Demand: Suppliers of a certain computer game will supply none at a price of $20 or lower. They will supply 100 at a price of $60. Consumers will purchase 500 when the price is $30. For each increase of $5 in the price, 50 fewer can be sold.

a) Find the linear supply equation.

b) Find the linear demand equation.

c) Find the equilibrium quantity and price.

d) Graph the lines and label the equilibrium point.

4. Humiture is a measure of our stress and discomfort at different temperatures and humidities. In the first data set, x is the humidity and y is the humiture if the temperature is 100 degrees Fahrenheit.

X=humidity 10% 20% 30% 40% 50% 60%

Y=humiture 85 92 99 105 111 118

a) Find the best fitting linear regression line and predict the humiture if the temperature is still 100 degrees but the humidity is 70%.

b) If the humidity increases by 5%, what is the change in humiture when the temp is 100 degrees?

The second data set is for a temperature of 90 degrees Fahrenheit

X=humidity 10% 20% 30% 40% 50% 60%

Y=humiture 73 79 84 88 93 97

a) Find the best fitting linear regression line and predict the humiture for 70% humidity when the temp is 90 degrees.

b) If the humidity increases by 5%, what is the change in humiture when the temp is 90 degrees?