Given that:
- Lucy must have the construction job done within 30 days.
- The bid of the first engineer is $2050 per hour, 8 hours per day.
- The bid of the second engineer is 1¢ per day which will double each day.
Let be "x" the number of days of work and "y" the total cost (in dollars)
• Using the data given, you can set up this equation to represent the bid of the first engineer:
[tex]\begin{gathered} y=(2050)(8)x \\ \\ y=16400x \end{gathered}[/tex]
And you can set up this equation to represent the bid of the second engineer:
[tex]y=0.01(2)^{x-1}[/tex]
• In order to graph them, you can give values to the variable "x" and evaluate, in order to get the corresponding y-values.
By substituting this value into the first equation:
[tex]\begin{gathered} \\ x=5 \\ \\ x=10 \end{gathered}[/tex]
You get:
[tex]y=16400(5)=82000[/tex][tex]y=16400(10)=164000[/tex]
- For the second equation, substitute this value:
[tex]x=20[/tex]
And evaluate:
[tex]y=0.01(2)^{20-1}=5242.88[/tex]
Now you can graph them:
You can identify in the graph that the total cost is greater in the first line than the cost in the second line. Therefore, the cost of the bid given for the first engineer will be greater.
Hence, the answer is:
• Equation 1st:
[tex]y=16400x[/tex]
• Equation 2nd:
[tex]y=0.01(2)^{x-1}[/tex]
• Graph:
• Better deal: The bid of the second engineer (the graph shows that the total cost using this deal will be less than the total cost using the first deal).
