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You are working part-time for an electronics company while going to high school. The following table shows the hourly wage, [tex]$w(t)$[/tex], in dollars, that you earn as a function of time, [tex]$t$[/tex]. Time is measured in years since the beginning of 2004 when you started working.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
TIME, [tex]$t$[/tex], Years since 2004 & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
Hourly wage, [tex]$w(t)$[/tex] & 9.00 & 9.90 & 10.90 & 12.00 & 13.20 & 14.50 \\
\hline
\end{tabular}

What is the growth factor?

A. 0.90
B. 1.0
C. 1.1
D. 1.2

Please select the best answer from the choices provided.



Answer :

GinnyAnswer
To find the growth factor of your hourly wage over time, we need to analyze the sequence of wages given for different years and see by what factor the wage increases each year.

The following are the hourly wages you earned over those years:
- Time [tex]\( t = 0 \)[/tex] years (2004): [tex]$9.00 - Time \( t = 1 \) year: $[/tex]9.90
- Time [tex]\( t = 2 \)[/tex] years: [tex]$10.90 - Time \( t = 3 \) years: $[/tex]12.00
- Time [tex]\( t = 4 \)[/tex] years: [tex]$13.20 - Time \( t = 5 \) years: $[/tex]14.50

### Step-by-Step Solution:

1. Calculate the growth factors between consecutive years:
- Growth factor from [tex]\( t = 0 \)[/tex] to [tex]\( t = 1 \)[/tex]: [tex]\( \frac{9.90}{9.00} \)[/tex]
- Growth factor from [tex]\( t = 1 \)[/tex] to [tex]\( t = 2 \)[/tex]: [tex]\( \frac{10.90}{9.90} \)[/tex]
- Growth factor from [tex]\( t = 2 \)[/tex] to [tex]\( t = 3 \)[/tex]: [tex]\( \frac{12.00}{10.90} \)[/tex]
- Growth factor from [tex]\( t = 3 \)[/tex] to [tex]\( t = 4 \)[/tex]: [tex]\( \frac{13.20}{12.00} \)[/tex]
- Growth factor from [tex]\( t = 4 \)[/tex] to [tex]\( t = 5 \)[/tex]: [tex]\( \frac{14.50}{13.20} \)[/tex]

2. Simplify these fractions:
- [tex]\( \frac{9.90}{9.00} = 1.1 \)[/tex]
- [tex]\( \frac{10.90}{9.90} \approx 1.1 \)[/tex]
- [tex]\( \frac{12.00}{10.90} \approx 1.1 \)[/tex]
- [tex]\( \frac{13.20}{12.00} \approx 1.1 \)[/tex]
- [tex]\( \frac{14.50}{13.20} \approx 1.1 \)[/tex]

3. Determine the most common growth factor.
From these calculations, we can see that the growth factor between each year is consistently around [tex]\( 1.1 \)[/tex].

Therefore, the growth factor is:

D. [tex]\( 1.1 \)[/tex]

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