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Two models R1 and R2 are given for revenue (in billions of dollars per year) for a large corporation. The model R1 gives projected annual revenues from 2008 through 2015, with t = 8 corresponding to 2008, and R2 gives projected revenues if there is a decrease in the rate of growth of corporate sales over the period. Approximate the total reduction in revenue if corporate sales are actually closer to the model R2. (Round your answer to three decimal places.) R1 = 7.21 + 0.55t R2 = 7.21 + 0.44t

User Adam Davis
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2 Answers

1 vote

Final answer:

The total reduction in revenue between the two models from 2008 to 2015 is calculated by finding the difference in revenue for each year (R1 - R2 = 0.11t) and summing these values from t = 8 to t = 15, after which the result is rounded to three decimal places.

Step-by-step explanation:

The student's question asks for the approximate total reduction in revenue, between models R1 and R2, from 2008 to 2015. The formulas for R1 and R2 are given by:


  • R1 = 7.21 + 0.55t

  • R2 = 7.21 + 0.44t

To find the total reduction in revenue, we need to calculate the difference in projected revenues between the two models for each year from t = 8 (2008) to t = 15 (2015) and sum these differences.

First, we'll calculate the difference for each year, which is (R1 - R2) = (0.55t - 0.44t) = 0.11t.

Now, we sum the differences from t = 8 to t = 15:

Total Reduction = ∑ from t=8 to t=15 (0.11t)

Performing this calculation, we get:

Total Reduction = (0.11 * 8) + (0.11 * 9) + ... + (0.11 * 15)

This results in a value that we need to round to three decimal places to get the final answer.

Each of the amounts calculated above represents the reduction in billions of dollars for each corresponding year.

User Gary Willoughby
by
5.7k points
0 votes

Answer:

7.0422 is the correct answer to the given question .

Step-by-step explanation:

Given

R1 = 7.21 + 0.55t

R2 = 7.21 + 0.44t

Decrease in the revenue can be determined by the formula


= Reduction\ in\ R1\ -\ Reduction\ in\ R2


= (7.21 + 0.55t ) - (7.21 + 0.44t)

=0.11 t

Now overall Reduction can be determined by the interval from t=8 to t=15

Consider c=0.11 t


(dc)/(dt)=0.11

Now integrated the equation from t=8 to t=15 to determine total reduction in revenue


=\int_(8)^(15)√(1+0.11^2)\ dL


=7.0422

User Matt Kenefick
by
5.8k points
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