Questions: A company's office supply expenses increase by 10% each year. The function C is used to calculate the cost of office expenses for each year. For example, C(2007) is 10,100 Office Supply Costs Year (y) Cost (C(y)) 2007 10,100 2008 11,110 2009 12,221 2010 13,443 2011 14,787 2012 16,266 2013 17,893 2014 19,682 2015 21,650 2016 23,815 2017 26,197 Which statement about the table above is accurate? C(2012) is 16,266. C(2009) added to 10% of C(2009) is C(2008). C(2014) is 10% of C(2013). C(26,197) is 2017.

A company's office supply expenses increase by 10% each year. The function C is used to calculate the cost of office expenses for each year. For example, C(2007) is 10,100
Office Supply Costs
Year (y) Cost (C(y))
2007 10,100
2008 11,110
2009 12,221
2010 13,443
2011 14,787
2012 16,266
2013 17,893
2014 19,682
2015 21,650
2016 23,815
2017 26,197

Which statement about the table above is accurate?
C(2012) is 16,266.
C(2009) added to 10% of C(2009) is C(2008).
C(2014) is 10% of C(2013).
C(26,197) is 2017.

Transcript text: A company's office supply expenses increase by $10 \%$ each year. The function $C$ is used to calculate the cost of office expenses for each year. For example, C(2007) is $\$ 10,100$ Office Supply Costs \begin{tabular}{|l|l|} \hline Year $(\boldsymbol{y})$ & Cost $(\boldsymbol{C}(\boldsymbol{y})$ ) \\ \hline 2007 & $\$ 10,100$ \\ \hline 2008 & $\$ 11,110$ \\ \hline 2009 & $\$ 12,221$ \\ \hline 2010 & $\$ 13,443$ \\ \hline 2011 & $\$ 14,787$ \\ \hline 2012 & $\$ 16,266$ \\ \hline 2013 & $\$ 17,893$ \\ \hline 2014 & $\$ 19,682$ \\ \hline 2015 & $\$ 21,650$ \\ \hline 2016 & $\$ 23,815$ \\ \hline 2017 & $\$ 26,197$ \\ \hline \end{tabular} Which statement about the table above is accurate? $\mathrm{C}(2012)$ is $\$ 16,266$. $C(2009)$ added to $10 \%$ of $C(2009)$ is $C(2008)$. C(2014) is $10 \%$ of C(2013). $C(\$ 26,197)$ is 2017.

Solution

Solution Steps

To determine which statement about the table is accurate, we need to verify each statement against the given data and the rule that the office supply expenses increase by 10% each year.

Verify if $ C(2012) $ is \$16,266.
Verify if $ C(2009) $ added to 10% of $ C(2009) $ equals $ C(2008) $.
Verify if $ C(2014) $ is 10% of $ C(2013) $.
Verify if $ C(\$26,197) $ corresponds to the year 2017.

Step 1: Verify Statement 1

We check if $ C(2012) = 16266 $. From the table, we see that $ C(2012) = 16266 $. Thus, Statement 1 is accurate.

Step 2: Verify Statement 2

We need to verify if $ C(2009) + 0.1 \cdot C(2009) = C(2008) $. Calculating this gives: \[ C(2009) = 12221 \] \[ C(2009) + 0.1 \cdot C(2009) = 12221 + 0.1 \cdot 12221 = 12221 + 1222.1 = 13443.1 \] However, $ C(2008) = 11110 $. Since $ 13443.1 \neq 11110 $, Statement 2 is not accurate.

Step 3: Verify Statement 3

We check if $ C(2014) = 0.1 \cdot C(2013) $. Calculating this gives: \[ C(2014) = 19682 \] \[ 0.1 \cdot C(2013) = 0.1 \cdot 17893 = 1789.3 \] Since $ 19682 \neq 1789.3 $, Statement 3 is not accurate.

Step 4: Verify Statement 4

We check if $ C(2017) = 26197 $. From the table, we see that $ C(2017) = 26197 $. Thus, Statement 4 is accurate.