International Business Machines Corporation (IBM) is an American multi- national technology company headquartered in Armonk, New...

  
 
 

  

 

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International Business Machines Corporation (IBM) is an American multi- national technology company headquartered in Armonk, New York, with operations in over 170 countries. The company began in 1911, founded in Endicott, New York, as the Computing-Tabulating-Recording Company (CTR) and was renamed "International Business Machines" in 1924. IBM is incorporated in New York. IBM produces and sells computer hardware, middleware and software, and provides hosting and consulting services in areas ranging from mainframe computers to nanotechnology. IBM is also a major research organization, holding the record for most U.S. patents gen- erated by a business (as of 2020) for 27 consecutive years. IBM's annual revenue in tens of billions dollars can be approximated by the model (http://macrotrends.net) R(x) = .02x³.29x² + .92x +9.6 where r is the number of years since 2009 (r = 0 corresponds to 2009) valid for 0≤x≤9. Type this function on an input line using the Graphing Perspective in GeoGebra. 1. Fill in the four blanks: This model, R(x), is valid starting with the (corresponding to r=_ ) and ending with the year (corresponding to r=________) year 2. Use the given model, R(z), to determine IBM's annual revenue for 2013. Fill in the blanks and write a sentence summarizing your answer. (a) R() = (b) IBM's 2013 Revenue (round to two decimal places) (c) Type a sentence summarizing your answer below: 3. Use the given model R(x) to determine IBM's annual revenue for 2014. Fill in the blanks and write a sentence summarizing your answer. (a) R(____) = (round to two decimal places) (b) IBM's 2014 Revenue = $ (c) Type a sentence summarizing your answer below: (d) Below is a portion of the graph of R(r) near the points corresponding to z = 4 and r= 5. Notice that IBM's revenue decreases from the year corresponding to a = 4 to the year corresponding to z = 5. The amount of decrease can be found by calculating R(5) - R(4), which will be negative (indicated by the downward pointing arrow). 3 (4, R(4)) a increases by 1 unit (one year increase) IBM's Revenue: R(x)=.02x³.29x²+.92x +9.6 Fill in the blanks below: • R(5)-R(4)= to . Interpretation of R(5) - R(4): IBM's annual revenue by $ (year). (5, R(5)) R(5)-R(4) <0 5 (correct to two decimal places) (increased or decreased) from (year) 4. The change in revenue, R(5) - R(4), calculated above can be approx- imated using the slope of the tangent line to R(z) at z = 4. Below is the same portion of the graph of R(r) along with it's tangent line at the point (4, R(4)). The tangent line is virtually indistinguishable from the graph of R(r) near r=4. Because of this, the slope of this tangent line tells us approximately how far we have to move down vertically from (4, R(4)) to get the point (5, R(5). Notice how close the points (5, R(5)) (on the graph of R(x)) and the point (5,9.48) (on the tangent line) are to each other. (4, R(4)) IBM's Revenue: R(x) = .02³.29x² +.92 +9.6 t(a)= tangent line at = 4. (a) Change in y= Ay = Units for Ay: (b) Change in z = * = dr = Units for Ar: increases by 1 unit (one year increase) Using the points (4, R(4)) and (5,9.48) on the tangent line, t(r), find its slope m by filling in the blanks below. Include units. Upon inspection of the graphs, you should expect m (the length of the green dotted line (but negative)) to be very close to R(5) R(4) (the length of the red dotted line in #3 (also negative)). (c) Slope of t(x) = m = Units for m: per increase of one- t(x) Ay Ar (5, R(5)) tangent line slope: m <0 (5,9.48) 5 (d) The slope, m, of the tangent line t(x) approximates IBM's change in revenue in (units) (units). International Business Machines Corporation (IBM) is an American multi- national technology company headquartered in Armonk, New York, with operations in over 170 countries. The company began in 1911, founded in Endicott, New York, as the Computing-Tabulating-Recording Company (CTR) and was renamed "International Business Machines" in 1924. IBM is incorporated in New York. IBM produces and sells computer hardware, middleware and software, and provides hosting and consulting services in areas ranging from mainframe computers to nanotechnology. IBM is also a major research organization, holding the record for most U.S. patents gen- erated by a business (as of 2020) for 27 consecutive years. IBM's annual revenue in tens of billions dollars can be approximated by the model (http://macrotrends.net) R(x) = .02x³.29x² + .92x +9.6 where r is the number of years since 2009 (r = 0 corresponds to 2009) valid for 0≤x≤9. Type this function on an input line using the Graphing Perspective in GeoGebra. 1. Fill in the four blanks: This model, R(x), is valid starting with the (corresponding to r=_ ) and ending with the year (corresponding to r=________) year 2. Use the given model, R(z), to determine IBM's annual revenue for 2013. Fill in the blanks and write a sentence summarizing your answer. (a) R() = (b) IBM's 2013 Revenue (round to two decimal places) (c) Type a sentence summarizing your answer below: 3. Use the given model R(x) to determine IBM's annual revenue for 2014. Fill in the blanks and write a sentence summarizing your answer. (a) R(____) = (round to two decimal places) (b) IBM's 2014 Revenue = $ (c) Type a sentence summarizing your answer below: (d) Below is a portion of the graph of R(r) near the points corresponding to z = 4 and r= 5. Notice that IBM's revenue decreases from the year corresponding to a = 4 to the year corresponding to z = 5. The amount of decrease can be found by calculating R(5) - R(4), which will be negative (indicated by the downward pointing arrow). 3 (4, R(4)) a increases by 1 unit (one year increase) IBM's Revenue: R(x)=.02x³.29x²+.92x +9.6 Fill in the blanks below: • R(5)-R(4)= to . Interpretation of R(5) - R(4): IBM's annual revenue by $ (year). (5, R(5)) R(5)-R(4) <0 5 (correct to two decimal places) (increased or decreased) from (year) 4. The change in revenue, R(5) - R(4), calculated above can be approx- imated using the slope of the tangent line to R(z) at z = 4. Below is the same portion of the graph of R(r) along with it's tangent line at the point (4, R(4)). The tangent line is virtually indistinguishable from the graph of R(r) near r=4. Because of this, the slope of this tangent line tells us approximately how far we have to move down vertically from (4, R(4)) to get the point (5, R(5). Notice how close the points (5, R(5)) (on the graph of R(x)) and the point (5,9.48) (on the tangent line) are to each other. (4, R(4)) IBM's Revenue: R(x) = .02³.29x² +.92 +9.6 t(a)= tangent line at = 4. (a) Change in y= Ay = Units for Ay: (b) Change in z = * = dr = Units for Ar: increases by 1 unit (one year increase) Using the points (4, R(4)) and (5,9.48) on the tangent line, t(r), find its slope m by filling in the blanks below. Include units. Upon inspection of the graphs, you should expect m (the length of the green dotted line (but negative)) to be very close to R(5) R(4) (the length of the red dotted line in #3 (also negative)). (c) Slope of t(x) = m = Units for m: per increase of one- t(x) Ay Ar (5, R(5)) tangent line slope: m <0 (5,9.48) 5 (d) The slope, m, of the tangent line t(x) approximates IBM's change in revenue in (units) (units).

Answer rating: 100% (QA)

ANSWER Given revenue function is 3 R2 002x 029x 092x916 2009 where ... View the full answer