Exploring Functions:

  1. Oil is starting to leak from a tanker. The following table indicates the volume of oil in the tanker at various times.

Time (hours) / 1.3 / 2.5 / 4.9 / 6.8 / 7.1 / 9.3 / 10.2
Volume
(cubic feet) / 3150.46 / 2735.5 / 1905.58 / 1248.56 / 1144.82 / 384.06 / 72.84

Using a graphing calculator or Graphical Analysis answer the following:

a)Sketch a graph of the function. Be sure to label the axes.

b)Describe the kind of function that is represented by this data: ______

c)State a reasonable domain______

and a reasonable range ______for this data

d)Write an equation that models this data: ______

e)Using the equation, determine how much oil was in the tanker before it began to leak. ______

f)How long will it take all the oil to leak out of the tanker? ______

  1. A scientist observes the growth of a certain bacteria. The following table indicates the number of bacteria per cubic millimeter at various times.

Time (days) / 0.7 / 1.3 / 1.8 / 2.1 / 2.7 / 3.5 / 3.9
Number per mm3 / 630.03 / 652.31 / 671.47 / 683.24 / 707.40 / 740.94 / 758.31

Using a graphing calculator or Graphical Analysis answer the following:

a)Sketch a graph of the function. Be sure to label the axes.

b)Describe the kind of function that is represented by this data: ______

c)State a reasonable domain______

and a reasonable range ______for this data

d)Write an equation that models this data: ______

e)Using the equation, determine how many bacteria will be present after five days.______

f)How many bacteria were present at the beginning? ______

g)How long will it take for the number of bacteria to increase to 6 times its original amount? ______

  1. The temperature of a cooling liquid over time is given in the following table.

Time (minutes) / 2 / 3 / 5 / 11 / 13 / 15 / 18
Temperature (Celsius) / 90.46 / 85.38 / 79.04 / 70.88 / 69.52 / 68.46 / 67.25

Using a graphing calculator or Graphical Analysis answer the following:

a)Sketch a graph of the function. Be sure to label the axes.

b)Describe the kind of function that is represented by this data: ______

c)State a reasonable domain______

and a reasonable range ______for this data

d)Write an equation that models this data: ______

e)Using the equation, determine the initial temperature of the liquid. ______

f)What will the temperature be after 1 hour? ______

g)To what final temperature does the liquid cool? ______

  1. In measuring the force a moving object has when it hits a stationary object, the students in Mr. Jamestons physics class collected the following data.

Distance
(inches) / 30 / 55 / 89 / 112 / 134 / 189 / 201
Force
(newtons) / 12.60 / 17.06 / 21.70 / 24.34 / 26.62 / 31.62 / 32.61

Using a graphing calculator or Graphical Analysis answer the following:

h)Sketch a graph of the function. Be sure to label the axes.

i)Describe the kind of function that is represented by this data: ______

j)State a reasonable domain______

and a reasonable range ______for this data

k)Write an equation that models this data: ______

l)Using the equation, determine how much force an object will have when it is 6 feet from the point of impact. ______

m)How far away from the point of impact should an object be so that it strikes with a force of 40 newtons? ______

SATEC/Algebra II/Linear Functions/2.09 Exploring Functions/Rev. 7-01Page 1 of 4