Diagnostic Test 1: basic algebra, functions, and graphs

Tommy's Fiat can drive 225 miles at 45 mph before it runs out of gas. It has a 15-gallon tank (that leaks!). Before starting to leak, the car got 30 mpg when driving at 45 mph. How many gallons per hour does the car leak fuel?

F(x) = 5x^(4/3). Find f(s^3).

F(x) = 5x^(4/3). Find f( 5^(-3/4) ).

Each year, a machine initially worth $30,000 depreciates 2% of its previous year's value. Find a function that expresses the machine's value after t years

How many years will it take until the machine value (at year end) has fallen below $25,000?

Consider the usual Cartesian plan (the x-y plane). Suppose y=f(x) is an arbitrary function and c is a constant. Select all the true statements.

Ford Motor Company manufactures cars and has plants in Charleston and Cleveland. At the Charleston plant, fixed costs equal $1,000,000 per month and the cost of producing each car is $6,400. At the Cleveland plant, fixed costs equal $1,200,000 per month and the cost of producing each car is $5000. For October 2013, the demand for Ford’s cars is forecasted to be 1,100. How many cars must be manufactured (in October 2013) at each plant if we want the total cost per month (fixed cost and variable cost) at both plants to be equal and the demand to be fully satisfied?

Calculate the total variable costs of manufacturing at each of the plants.