Download Exponential Functions 4

Math 30-2
Exponential Functions: Lesson #4
Exponential Regression
Objective: By the end of this lesson, you should be able to:
- graph data on a calculator and find the exponential regression equation that best
approximates that data
- solve a contextual problem involving exponential data
You can use your calculator to graph exponential data and find the exponential function of best
fit in the form y  a  b x .
Recall: To Enter Data into a List:
STAT 1:Edit
To Graph a Scatter Plot:
Turn on Plot 1
Set appropriate window settings:
- manually in WINDOW or
- ZOOM 9:ZoomStat
To Calculate an Exponential Regression Equation:
STAT ► CALC 0:ExpReg
To Graph the Regression Equation:
Y= VARS, 5: Statistics, ►► EQ, 1: RegEQ
e.g. 1) Sonja did an experiment to determine the cooling curve of water. She poured nearly
boiling water into a cup, then recorded the temperature of the water in the cup as it cooled
over time. Her data is shown below.
Time (min)
Temperature (°C)
0
90
5
78
a) Graph the data on the grid below.
10
68
20
52
30
38
45
26
Math 30-2
Exponential Functions: Lesson #4
b) Before performing an exponential regression, what do you expect the a value to be in
the equation y  a  b x ? Will the base, b, be greater than 1 or between 0 and 1?
Explain.
c) Perform an exponential regression to find the equation of the curve. Round the
values to four decimal places. Evaluate your predictions from part b.
d) What was the approximate temperature, to the nearest degree, after 15 minutes?
e) At what time, to the nearest minute, did the temperature of the water reach 40°C?
f) By what percent is the water cooling each minute?
e.g. 2) Markus put $2000 into a bank account that pays compound interest, compounded
annually. He kept track of the value of his investment over the next 5 years, as shown:
Time (years)
Amount ($)
0
2000.00
1
2065.00
2
2132.11
3
2201.41
a) Perform an exponential regression and write the equation.
b) What rate of interest is Markus earning on his investment?
c) How much will his investment be worth in 9 years?
4
2272.95
5
2346.82
Math 30-2
Exponential Functions: Lesson #4
Notice: In the equation y  a  b x

a is the ________________________________

b is the ______________________________________________________
e.g. 3) A researcher is investigating mould growing in a petri dish in her laboratory. When first
observed, the mould covered only 2.5% of the dish’s surface. After 1 day, the surface
area of the mould doubled in size, as shown in the table below.
Day
0
1
Area Covered (%)
2.5
5
a) If the mould continues to double in size every day, continue the table above.
b) Write the equation that models this exponential function without using a calculator.
c) If the mould continues to grow at the same rate, how long in days and hours will it
take for the petri dish to be completely covered with mould? Round to the nearest
hour.
Assignment:
p. 377-381 #3-9, 11-14
p. 396 #5-7