CA Chapter 2 Work
1. A maximum recommended slope of a wheelchair ramp is 1/12. A business installs a ramp that rises 36 inches over a horizontal length of 32 feet. Is the ramp steeper than recommended? How do you know?
2. An accounting firm determines that the value V (in dollars) of a copier t years after its purchase is given by V= -300t XXXXXXXXXXInterpret the y-intercept and slope of this line. What does it mean?
3. A manufacturing firm purchases a machine worth $24,750. The machine has a useful life of 6 years. After 6 years, the machine will have to be discarded and replaced, because it will have no salvage value. Write a linear equation that describes the book value of the machine each year.
4. The sales for NIKE were approximately $6.5 B in 2013 and $7.3 B in 2014. Using only this information, write a linear equation that gives the sales in terms of the year. Then predict sales in year 2017.
5. A pharmaceutical salesperson receives a salary of $5000 a month plus a commission or 7% of sales. Write a linear equation for the salesperson’s monthly wages, W, in terms of monthly sales, S.
6. The number, N, of bacteria in a refrigerated food is given by
N(T) = 8T²-14T +200, 2 ≤ T≤ 12. Where T is the temperature of the food in degrees C.
When the food is removed from the refrigerator, the temperature of the food is given by
T(t)=2t + 2, 0 ≤ t ≤ 5, where t is time in hours.
a) Find (Nâ—¦T)(t)
b) Find the time when bacteria count reaches 1000.
7. Your wage is $10 an hour plus $0.75 for each unit produced per hour. So, your hourly wage y in terms of the number of units produced x is y=10 + .075x.
a) Find the inverse function. What does each variable represent in the inverse function?
b) Determine the number of units produced with your hourly wage is $24.25.
8. A discount outlet offers a 20% discount on all items. Write a linear equation giving the sale price S for an item with a list price of L.
9. A manuscript translator charges a starting fee of $50 plus $2.50 per page translated. Write a linear equation for the amount A earned for translating p pages.
10. It costs a company $58 to produce 6 units of a product and $78 to produce 10 unites. Assuming that the cost function is linear, how much does it cost to produce 25 units?
11. For groups of 60 or more people, a charter bus company determines the rates per person according to the formula
Rate= 10 – 0.05(n-60), n≥60. Where the rate is given in dollars and n is the number of people.
a) Write the revenue R as a function of n.
b) Graph the linear equation and tell the approximate number of people that will maximize the revenue.