Pre-CalculusPacket1DueThursday,February11th2016

1. A tank holds 50 gal of water, which drains from a leak at the bottom, causing the tank to empty in�20 min. The tank drains faster when it is nearly full because the pressure on the leak is greater. Torricelli’s Law gives the volume of water remaining in the tank after t minutes as

! " = 50 1 − "20

*0 ≤ " ≤ 20

a. FindV(0)andV(20)b. Whatdoyouranswerstopart(a)represent?c. MakeatableofvaluesV(t)fort=0,5,10,20d. FindthenetchangeofthevolumeVastchangesfrom0to20min.

2. As blood moves through a vein or an artery, it’s velocity v is greatest along the central axis and decreases as the distance r from the central axis increases (see the figure). The formula that gives v as a function of r is called the law of laminar ow. For an artery with radius 0.5 cm, the relationship between v (in cm/s) and r (in cm) is given by the function

18,500 0.25 − /* 0 ≤ /≤ 0.5

a. Findv(0.1)andv(0.4)b. Whatdoyouranswerstopart(a)tellyouabouttheflowofbloodintothis

artery?c. Makeatableofvaluesofv(r)forr=0,0.1,0.2,0.3,0.4,0.5d. Findthenetchangeinthevelocityvasrrangesfrom0.1cmto0.5cm

3. You place a frozen pie in an oven and bake it for an hour. Then you take the pie out and let it cool before eating it. Sketch a rough graph of the temperature of the pie as a function of time.

4. Westside Energy charges its electric customers a base rate of $6.00 per month, plus 10¢ per kilowatt-hour (kWh) for the first 300 kWh used and 6¢ per kWh for all usage over 300 kWh. Suppose a customer uses x kWh of electricity in one month.

a. Express the monthly cost E as a piecewise defined function of x. b. Graph the function E for 0 ≤ 0 ≤ 600

5. Graphingtheabsolutevalueofafunction(Clueusewww.desmos.com)

a. Drawthegraphsofthefunctions2 0 = 0* + 0 − 6and4 0 = |0* + 0 − 6|

Howarethegraphsrelated?

b. Drawthegraphsof2 0 = 06 − 60*and4 0 = |06 − 60*|.Howarethegraphsoffandgrelated?

c. Ingeneral,ifg(x)=f(x),howarethegraphsoffandgrelated.Beclear!

6. The graph shows the vertical acceleration of the ground from the 1994 Northridge earthquake in Los Angeles, as measured by a seismograph. (Here t represents the time in seconds.)

a. At what time t did the earthquake first make noticeable movements of the earth? b. At what time t did the earthquake seem to end?� c. At what time t was the maximum intensity of the earthquake reached?

7. Three runners compete in a 100-meter hurdle race. The graph depicts the distance run as a function of time for each runner. Describe in words what the graph tells you about this race. Who won the race? Did each runner finish the race? What do you think happened to Runner B?

8. Vertical Line Test: domain and Range Use the Vertical Line Test to determine whether the curve is a graph of a function of x. If it is, state the domain and range of the function.