Answer
$a.\displaystyle \qquad\frac{23}{25}$
$ b.\qquad$The model overestimates the data for 2014 by $\displaystyle \frac{1}{50}$
$c.\displaystyle \qquad\frac{19}{20}$
Work Step by Step
$a.$
Substitute $14$ for x ($2014$ was 10 years after 2000):
$I=\displaystyle \frac{3}{100}\cdot 14+\frac{1}{2}=$... reduce the product by $2$
$=\displaystyle \frac{3\cdot 7}{50}+\frac{1}{2}\qquad$... LCD is $50$
$=\displaystyle \frac{21}{50}+\frac{1\times 25}{2\times 25}$
$=\displaystyle \frac{21+25}{50}$
$=\displaystyle \frac{46}{50}\qquad $... reduce by 2
$=\displaystyle \frac{23}{25}$
$b.$
The graph shows the fraction to be $\displaystyle \frac{9}{10}$.
The LCD for 10 and 50 is $50$.
Model: $\displaystyle \frac{23\times 2}{25\times 2}=\frac{46}{50}$
Graph: $\displaystyle \frac{9\times 5}{10\times 5}=\frac{45}{50}$
(The model overestimates the data for 2014 by $\displaystyle \frac{1}{50}$)
$c.$
Substitute $15$ for x ($2015$ was $15$ years after 2000):
$I=\displaystyle \frac{3}{100}\cdot 15+\frac{1}{2}=$... reduce the product by $5$
$=\displaystyle \frac{3\cdot 3}{20} +\frac{1}{2}$
$=\displaystyle \frac{9}{20} +\frac{1}{2}\qquad$... LCD is $20$
$=\displaystyle \frac{9}{20}+\frac{1\times 10}{2\times 10}$
$=\displaystyle \frac{9+10}{20}$
$=\displaystyle \frac{19}{20}$
