1. The value of a machine depreciates by an equal amount each year of its useful life. Suppose the machine was purchased for $18,000 and has a useful life of five years, after which time it has a scrap value of $2,000.
(a) Identify the x-variable and the y-variable.
(b) Construct the data table for this problem.
(c) Find the equation of the linear model.
(d) What is the annual depreciation rate?
(e) What is the value of the machine two and one-half years after its purchase?
(f) When will the value of the machine be $6,000?
Give your final answer in terms of years and months.
2. There are two common units of measurement for temperature: degrees Fahrenheit (ºF) and degrees Celsius (ºC).
Water freezes at: 0 ºC and 32 ºF
Water boils at: 100 ºC and 212 ºF
Can we derive a linear formula by converting from ºF to ºC and back again? Of course we can!
(a) Use the above data to find a formula for ºF as a function of ºC
Hint: leave m as a fraction
Hint Hint: F as a function of C is the same thing as x as a function of y, so here, your F is your x and C is your y.
(b) Use the above data to find a formula for ºC as a function of ºF
Hint: leave m and b as functions
(c) Use the formula from (a) and algebraic manipulation to find a formula for ºC as a function of ºF.
Compare your answer from (b)
(d) You are going on a business trip to Bzwakii, where the average temperature is 11 ºC. How should you dress?
(e) You are sending a recipe for Butterscotch Brownies to your friend in Canada. Your recipe calls for the brownies to be baked at 350 ºF, What is the equivalent temp in ºC?