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sattari [20]
3 years ago
11

10 points eBookReferencesCheck my workCheck My Work button is now enabled1Item 9 Consider the following observations of a series

: Year 1 Year 2 Year 3 Year 4 100 120 160 170 a. Calculate the growth rates for Year 1–Year 2, Year 2–Year 3, and Year 3–Year 4. (Round your answers to 4 decimal places.) b. Calculate the average growth rate. (Enter your answer as a percentage, rounded to 2 decimal places, using intermediate calculations rounded to at least 4 decimal places.)
Mathematics
1 answer:
alexandr402 [8]3 years ago
3 0

Answer:

Growth\ Rate = 0.2000 --- Year 1 to 2

Growth\ Rate = 0.3333 --- Year 2 to 3

Growth\ Rate = 0.0625 --- Year 3 to 4

Average\ Growth\ Rate = 19.86\%

Step-by-step explanation:

Given

\begin{array}{cc}{Year\ 1} & {100} & {Year\ 2} & {120} & {Year\ 3} & {160} & {Year\ 4} & {170} \ \end{array}

Solving (a): Growth Rates between each year

For Year 1 to 2.

Growth\ Rate = \frac{Year\ 2 - Year\ 1}{Year\ 1}

Growth\ Rate = \frac{120-100}{100}

Growth\ Rate = \frac{20}{100}

Growth\ Rate = 0.2000

For Year 2 to 3.

Growth\ Rate = \frac{Year\ 3 - Year\ 2}{Year\ 2}

Growth\ Rate = \frac{160-120}{120}

Growth\ Rate = \frac{40}{120}

Growth\ Rate = 0.3333

For Year 3 to 4.

Growth\ Rate = \frac{Year\ 4 - Year\ 3}{Year\ 3}

Growth\ Rate = \frac{170-160}{160}

Growth\ Rate = \frac{10}{160}

Growth\ Rate = 0.0625

Solving (b): The average growth rate

This is calculated as by calculating the mean value of the growth rates in (a)

Average\ Growth\ Rate = \frac{1}{3}(0.2000 + 0.3333 + 0.0625)

Average\ Growth\ Rate = \frac{1}{3}(0.5958)

Average\ Growth\ Rate = \frac{1}{3}*0.5958

Average\ Growth\ Rate = 0.1986

Convert to percentage

Average\ Growth\ Rate = 0.1986 * 100\%

Average\ Growth\ Rate = 19.86\%

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