Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Let's determine Carlos's salary for each job offer after \( t \) years.
### Job Offer 1: Fixed $4380 Raise Per Year
For this job, Carlos receives a fixed annual raise of $4380. The formula to calculate the salary after \( t \) years is:
[tex]\[ \text{Salary} = \text{Starting Salary} + (\text{Fixed Annual Raise} \times t) \][/tex]
Given:
- Starting salary \( = \$73000 \)
- Fixed annual raise \( = \$4380 \)
Let's calculate the salary for \( t = 1 \), \( t = 5 \), \( t = 10 \), and \( t = 15 \) years:
1. After 1 year:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 1) = \$77380
\][/tex]
2. After 5 years:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 5) = \$94900
\][/tex]
3. After 10 years:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 10) = \$116800
\][/tex]
4. After 15 years:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 15) = \$138700
\][/tex]
### Job Offer 2: 5% Raise Per Year
For this job, Carlos receives an annual raise of 5% of his current salary. The formula to calculate the salary after \( t \) years is:
[tex]\[ \text{Salary} = \text{Starting Salary} \times (1 + \text{Percent Annual Raise})^t \][/tex]
Given:
- Starting salary \( = \$73000 \)
- Percent annual raise \( = 0.05 \)
Let's calculate the salary for \( t = 1 \), \( t = 5 \), \( t = 10 \), and \( t = 15 \) years:
1. After 1 year:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^1 = \$[/tex]76650
\][/tex]
2. After 5 years:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^5 = \$[/tex]93169
\][/tex]
3. After 10 years:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^{10} = \$[/tex]118909
\][/tex]
4. After 15 years:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^{15} = \$[/tex]151762
\][/tex]
### Summary Tables
Here are the completed tables for both job offers:
#### Salary with $4380 Raise Per Year
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] years & 1 & 5 & 10 & 15 \\
\hline
\begin{tabular}{c} Salary with \\ [tex]$4380$[/tex] raise \\ per year \end{tabular} & [tex]$77380 & $[/tex]94900 & [tex]$116800 & $[/tex]138700 \\
\hline
\end{tabular}
#### Salary with 5% Raise Per Year
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] years & 1 & 5 & 10 & 15 \\
\hline
\begin{tabular}{c} Salary with \\ [tex]$5\%$[/tex] raise \\ per year \end{tabular} & [tex]$76650 & $[/tex]93169 & [tex]$118909 & $[/tex]151762 \\
\hline
\end{tabular}
This should give Carlos a clear understanding of his salary progression under each job offer over 15 years.
### Job Offer 1: Fixed $4380 Raise Per Year
For this job, Carlos receives a fixed annual raise of $4380. The formula to calculate the salary after \( t \) years is:
[tex]\[ \text{Salary} = \text{Starting Salary} + (\text{Fixed Annual Raise} \times t) \][/tex]
Given:
- Starting salary \( = \$73000 \)
- Fixed annual raise \( = \$4380 \)
Let's calculate the salary for \( t = 1 \), \( t = 5 \), \( t = 10 \), and \( t = 15 \) years:
1. After 1 year:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 1) = \$77380
\][/tex]
2. After 5 years:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 5) = \$94900
\][/tex]
3. After 10 years:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 10) = \$116800
\][/tex]
4. After 15 years:
[tex]\[ \text{Salary} = \[tex]$73000 + (\$[/tex]4380 \times 15) = \$138700
\][/tex]
### Job Offer 2: 5% Raise Per Year
For this job, Carlos receives an annual raise of 5% of his current salary. The formula to calculate the salary after \( t \) years is:
[tex]\[ \text{Salary} = \text{Starting Salary} \times (1 + \text{Percent Annual Raise})^t \][/tex]
Given:
- Starting salary \( = \$73000 \)
- Percent annual raise \( = 0.05 \)
Let's calculate the salary for \( t = 1 \), \( t = 5 \), \( t = 10 \), and \( t = 15 \) years:
1. After 1 year:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^1 = \$[/tex]76650
\][/tex]
2. After 5 years:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^5 = \$[/tex]93169
\][/tex]
3. After 10 years:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^{10} = \$[/tex]118909
\][/tex]
4. After 15 years:
[tex]\[ \text{Salary} = \[tex]$73000 \times (1 + 0.05)^{15} = \$[/tex]151762
\][/tex]
### Summary Tables
Here are the completed tables for both job offers:
#### Salary with $4380 Raise Per Year
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] years & 1 & 5 & 10 & 15 \\
\hline
\begin{tabular}{c} Salary with \\ [tex]$4380$[/tex] raise \\ per year \end{tabular} & [tex]$77380 & $[/tex]94900 & [tex]$116800 & $[/tex]138700 \\
\hline
\end{tabular}
#### Salary with 5% Raise Per Year
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$t$[/tex] years & 1 & 5 & 10 & 15 \\
\hline
\begin{tabular}{c} Salary with \\ [tex]$5\%$[/tex] raise \\ per year \end{tabular} & [tex]$76650 & $[/tex]93169 & [tex]$118909 & $[/tex]151762 \\
\hline
\end{tabular}
This should give Carlos a clear understanding of his salary progression under each job offer over 15 years.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.