Warm Up

1
Pg. 1
Warm Up Perform a quadratic regression on the
following data
x 1 2 6 11 13
f(x) 3 6 39 120 170
7-8 LEARNING GOALS
7.8.1 Model data by using exponential and
logarithmic functions. 7.8.2 Use exponential and
logarithmic models to analyze and predict.
f(x) 2(3x)
In previous chapters we analyzed common
_________________ to determine which polynomial
model best fits a data set..

• For exponential data sets the common
  _____________ of y-values is constant for
  ________________ spaced x-values.
• The data will fit an exponential model of this
  general form f(x) abx.
• The common ratio will be the base, ___ of the
  model and the y-intercept will be the
  coefficient, _____.

Example 1 Identifying Exponential Data
Determine whether f is an exponential function of
x of the form f(x) abx. If so, find the
constant ratio.
x 1 0 1 2 3
f(x) 16 24 36 54 81
x 1 0 1 2 3
f(x) 2 3 5 8 12
B.
A.
2
Pg. 2
Once you know that data are exponential, you can
use ExpReg (exponential regression) on your
calculator to find a function that fits. The
calculator fits exponential functions to abx, so
translations (up, down, right, and left) cannot
be modeled.
STAT ? Edit (Fill in L1 and L2) STAT ? Arrow to
the Right CALC ? ExpReg
Example 2 College Application
A. Use exponential regression to find a
function that models this data. When will the
number of bacteria reach 2000?
Time (min) 0 1 2 3 4 5
Bacteria 200 248 312 390 489 610
a b r2 r
f(x) __________________ 2000 bacteria in
_______ mins.
Many natural phenomena can be modeled by natural
log functions. You can use a (natural)
logarithmic regression to find a function.
Global Population Growth Global Population Growth
Pop. (billions) Year
1 1800
2 1927
3 1960
4 1974
5 1987
6 1999
STAT ? Edit (Fill in L1 and L2) STAT ? Arrow to
the Right CALC ? LnReg
Example 3 Application
A. Find a natural log model for the data.
According to the model, when will the global
population exceed 9,000,000,000?
f(x) __________________
Population exceeds 9 billion in year _______ .