6.2.5 Curve Fitting with Polynomial Models - Practice
2. The table shows the numbers of cars manufactured by a company for selected years. Write a polynomial function for cars manufactured in thousands where x represents the years since 1990. Year
1. Use finite differences to determine the degree of the polynomial that best describes the data.
x − 3 −1 1 3 5 7 y 4 6 1 − 11 − 30 − 56
1991 1993 1995 1997 1999
Cars manufactured (thousands)
1.4 11.4 39.8 96.2 190.2
4. The table shows the number of students graduating from a university in selected years. Use a calculator to write a cubic model for the number of graduates in a given year since 1990. Then use the model to estimate the number of graduates in 2001. Year
3. The table shows the numbers of ships that visited a port in the past 5 years. Write a polynomial function for the number of ships in thousands that visited the port in a given year. Year 1 2 3 4 5 Number of ships (thousands) 4.2 8.2 14.8 24 35.8
1993 1995 1996 1997 1999 2000
Number of Graduates
586 1260 1502 1498 2504 3710
5. The table shows the number of students graduating from an online university in selected years. Use a calculator to write a cubic model for the number of graduates in a given year since 2002. Then use the model to estimate the number of graduates in 2008. Year
6. The table shows the number of phones sold by a small cell phone provider in various years. Use a calculator to write a quartic model for the number of phones sold in a given year since 2000 and use the model to estimate the number of phones sold in 2014. Year 2005 2007 2008 2010 2012 2013 Number of Cell Phones 324 394 455 635 792 914
2003 2005 2006 2007 2009 2010
Number of Graduates
675 1349 1591 1587 2593 3799
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