Learning Resources
Lesson
The completion of this investigation will require you to seek help from your in school science teacher and the use of materials from the science lab. Care must be taken since boiling water is involved. A regular glass container is not recommended since it may crack with high heat, A flask from the science lab is more appropriate.
You will require
- kettle
- thermometer
- small Styrofoam block
- small container( not Styrofoam or glass)
- watch with a second hand
- graphing technology with regression analysis capabilities
It is recommended you work in a group of three, if possible. One can measure the time, another read the thermometer and the third record the data.
In Step A, it is important to record the room temperature since the water4 will not cool below this temperature. The water should cool down to room temperature.
For Step B the Styrofoam is used to keep the thermometer away from the sides of the flask since you want to record the changes in the water temperature only. Check to make sure that the Styrofoam does not completely cover the glass bulb of the thermometer.
In Step C enough boiling water should be used to cover approximately 2 cm of the thermometer - too much water will require a lengthy cooling time. Record your data in a table.
Complete the investigation questions from the Activities Section. After these are complete, what do you think the equation would be if the room temperature is 160C?
In the investigation you found that the horizontal asymptote for exponential functions is not always y = 0 (i.e. the x-axis). This is true for the function 
, but when, as in the situation modeled in the investigation, the graph approaches a different value the horizontal asymptote changes ( in the investigation the room temperature ). As a result the equation is changed to 
or in its transformational form of 
where y = d is the horizontal asymptote. Consider the graphical presentation of such graphs. In the demonstration below use the Go forward one frame button to step through the function 
and view how it changes as the d value changes. Use the Global Actions buttons to navigate the window or the Show button to see the graph as an animation.
From the above demonstration you should be able to see that the horizontal asymptote changes as the graph changes. Notice the relationship between the horizontal asymptote and the equation of the function.
Complete the Activities Section !
Activity
Investigation Questions p.139 - 140. Complete 40, 41 and 42
Think About p. 139
Check Your Understanding p.140 - 141. Complete 43, 44, 45, 46 and 47
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
Given the function
- Write it in its transformational form.
- Is it a growth or decay curve?
- Write the equation of its horizontal asymptote.
- What is its y-intercept?
- Using a table of values, determine if there is a common ratio between successive y-values.
Click here for solutions.