Answered

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Question 10 [3 points]
Revenues for Cantu Excavating have increased by 2.55%, 8.21%, 3.52 %, and 9.21% in the last four years. Calculate the annual average increase in
revenue. Give your answer as a percent accurate to at least two decimal places.
=
Average 0.00 %
​

Sagot :

sqdancefan

Answer:

  5.83%

Step-by-step explanation:

You want the average annual revenue increase over the 4-year period in which the annual increases were 2.55%, 8.21%, 3.52%, and 9.21%.

Multiplier

If p was the percentage increase in a given year, it means the revenue was multiplied by (1+p). Then the multiplier over the four years of concern would be ...

  (1 +p₁)·(1 +p₂)·(1 +p₃)·(1 +p₄)

Annual average

If the average annual percentage increase is x, then we have ...

  (1 +p₁)·(1 +p₂)·(1 +p₃)·(1 +p₄) = (1 +x)⁴

Solving for x gives ...

  [tex]x=\sqrt[4]{(1+p_1)(1+p_2)(1+p_3)(1+p_4)}-1[/tex]

The calculation of that value is shown in the attachment.

  x ≈ 0.5833 ≈ 5.83%

The average annual increase in revenue was about 5.83%.

View image sqdancefan
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