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# Sp00ex2 - Sp 00 EGN 3420 Exam 2 Name Show All Work Problem...

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Sp 00 EGN 3420 Exam 2 Name ________________________ Show All Work! Problem 1 (35 pts) A retail store owner is trying to determine the best price for a popular tee-shirt. He has been experimenting with different prices to assess its effect on sales. The following sales records have been accumulated over the past six weeks. Week No. 1 2 3 4 5 6 Shirt Price ( p ) \$3.00 \$6.00 \$5.25 \$3.75 \$3.50 \$4.75 Weekly Sales ( s ) 855 296 403 738 804 512 a) Find the coefficients a 0 , a 1 , .... , a 5 in the standard form of the interpolating polynomial 5 2 3 4 5 0 1 2 3 4 5 ( ) s p a a p a p a p a p a p = + + + + + by solving the 6 x 6 system of equations, Ax b = where x is the vector 0 1 2 3 4 5 [ ] . T a a a a a a You can use your calculator to find the solution. Express all answers in scientific notation with 4 places after the decimal point in the mantissa. b) Estimate the amount of weekly sales if the shirts are priced at \$5.00 each. c) Use the result of Part a) to estimate the weekly revenue r (Weekly Sales x Shirt Price) if the shirts are priced at \$4.00 each.

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Sp 00 EGN 3420 Exam 2 Name ________________________ Show All Work!
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