4.7E: Fitting Exponential Models to Data (Exercises)
 Page ID
 13911
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Graph each function on a semilog scale, then find a formula for the linearized function in the form \(\log \left(f\left(x\right)\right)=mx+b\). \[1. f\left(x\right)=4\left(1.3\right)^{x} 2. f\left(x\right)=2\left(1.5\right)^{x}\] \[3. f\left(x\right)=10\left(0.2\right)^{x} 4. f\left(x\right)=30\left(0.7\right)^{x}\]
The graph below is on a semilog scale, as indicated. Find a formula for the exponential function \(y(x)\).
5. 6.
7. 8.
Use regression to find an exponential function that best fits the data given.
9.  x 1 2 3 4 5 6 y 1125 1495 2310 3294 4650 6361 

10.  x 1 2 3 4 5 6 y 643 829 920 1073 1330 1631 
11.  x 1 2 3 4 5 6 y 555 383 307 210 158 122 
12.  x 1 2 3 4 5 6 y 699 701 695 668 683 712 

Total expenditures (in billions of dollars) in the US for nursing home care are shown below. Use regression to find an exponential function that models the data. What does the model predict expenditures will be in 2015?
Year  1990  1995  2000  2003  2005  2008 

Expenditure  53  74  95  110  121  138 

Light intensity as it passes through water decreases exponentially with depth. The data below shows the light intensity (in lumens) at various depths. Use regression to find an function that models the data. What does the model predict the intensity will be at 25 feet?
Depth (ft)  3  6  9  12  15  18 

Lumen  11.5  8.6  6.7  5.2  3.8  2.9 

The average price of electricity (in cents per kilowatt hour) from 1990 through 2008 is given below. Determine if a linear or exponential model better fits the data, and use the better model to predict the price of electricity in 2014.
Year  1990  1992  1994  1996  1998  2000  2002  2004  2006  2008 

Cost  7.83  8.21  8.38  8.36  8.26  8.24  8.44  8.95  10.40  11.26 

The average cost of a loaf of white bread from 1986 through 2008 is given below. Determine if a linear or exponential model better fits the data, and use the better model to predict the price of a loaf of bread in 2016.
Year  1986  1988  1990  1995  1997  2000  2002  2004  2006  2008 

Cost  0.57  0.66  0.70  0.84  0.88  0.99  1.03  0.97  1.14  1.42 