In a particular research database, the number of indexed genetics articles had increased by an average of $307$ articles per year for several years. At the end of that time period, there were $6000$ genetics articles indexed. Since then, the number of articles has increased by $8\%$ annually. To the nearest whole number, how many more genetics articles are there after $2$ years of this increase than if the growth rate had not changed? $\newline$ ◻

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Grade 8

Percent of change: word problems

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Q. In a particular research database, the number of indexed genetics articles had increased by an average of

307

articles per year for several years. At the end of that time period, there were

6000

genetics articles indexed. Since then, the number of articles has increased by

8\%

annually. To the nearest whole number, how many more genetics articles are there after

2

years of this increase than if the growth rate had not changed?

\newline

◻

Calculate Initial Growth Rate: Calculate the number of articles after $2$ years with the original growth rate of $307$ articles per year. $\newline$ Number of articles after $2$ years = Initial number of articles + (Growth per year $\times$ Number of years) $\newline$ = $6000$ articles + ( $307$ articles/year $\times$ $2$ years) $\newline$ = $6000$ articles + $614$ articles $\newline$ = $307$ $0$ articles
Calculate New Growth Rate: Calculate the number of articles after $2$ years with the new $8$ % annual growth rate. $\newline$ First, calculate the number of articles after the first year. $\newline$ Number of articles after $1$ year = Initial number of articles $\times$ ( $1$ + Growth rate) $\newline$ = $6000$ articles $\times$ $(1 + 0.08)$ $\newline$ = $6000$ articles $\times 1.08$ $\newline$ = $6480$ articles
Calculate Growth Rate After $2$ Years: Calculate the number of articles after the second year with the $8$ \% growth rate. $\newline$ Number of articles after $2$ years = Number of articles after $1$ year * $1 + \text{Growth rate}$ $\newline$ = $6480$ articles * $1 + 0.08$ $\newline$ = $6480$ articles * $1.08$ $\newline$ = $6998.4$ articles $\newline$ Since we need the nearest whole number, we round $6998.4$ to $6998$ articles.
Find Difference in Growth Rates: Find the difference in the number of articles after $2$ years between the two growth rates. $\newline$ Difference = Number of articles after $2$ years with $8\%$ growth - Number of articles after $2$ years with $307$ growth per year $\newline$ = $6998$ articles - $6614$ articles $\newline$ = $384$ articles