Question

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.)

Answer 1

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

$Average\ Growth\ Rate = 0.1986 * 100\%$

$Average\ Growth\ Rate = 19.86\%$