Job A:
The initial amount is $35 000
The amount of increase for each year is $1500
We can write an equation for this situation
Where x is the number of years
[tex]y_A=35000+1500x[/tex]Job B:
The initial amount is $30 000
The percent of the increase is 7%
Change it to decimal and find the factor of growth
[tex]\frac{7}{100}=0.07[/tex]The factor of growth = 1 + 0.07 = 1.07, then
The equation is
[tex]y_B=30000(1.07)^x[/tex]Let us complete the table
[tex]\begin{gathered} x=0 \\ y_A=35000+1500(0)=35000 \\ y_B=30000(1.07)^{0-1}=30000 \end{gathered}[/tex][tex]\begin{gathered} x=1 \\ y_A=35000+1500(1)=36500 \\ y_B=30000(1.07)^1=32100 \end{gathered}[/tex][tex]\begin{gathered} x=2 \\ y_A=35000+1500(2)=38000 \\ y_B=30000(1.07)^2=34347 \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ y_A=35000+1500(3)=39500_{} \\ y_B=30000(1.07)^3=36751.29 \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ y_A=35000+1500(4)=41000 \\ y_B=30000(1.07)^4=39323.88 \end{gathered}[/tex][tex]\begin{gathered} x=5 \\ y_A=35000+1500(5)=42500 \\ y_B=30000(1.07)^5=42076.55 \end{gathered}[/tex][tex]\begin{gathered} x=6 \\ y_A=35000+1500(6)=44000 \\ y_B=30000(1.07)^6=45021.9 \end{gathered}[/tex][tex]\begin{gathered} x=7 \\ y_A=35000+1500(7)=45500 \\ y_B=30000(1.07)^7=48173.44 \end{gathered}[/tex][tex]\begin{gathered} x=8 \\ y_A=35000+1500(8)=47000 \\ y_B=30000(1.07)^8=51545.59 \end{gathered}[/tex][tex]\begin{gathered} x=9 \\ y_A=35000+1500(9)=48500 \\ y_B=30000(1.07)^9=55153.78 \end{gathered}[/tex][tex]\begin{gathered} x=10 \\ y_A=35000+1500(10)=50000 \\ y_B=30000(1.07)^{10}=59014.54 \end{gathered}[/tex][tex]\begin{gathered} x=11 \\ y_A=35000+1500(11)=51500 \\ y_B=30000(1.07)^{11}=63145.56 \end{gathered}[/tex]Now let us compare between them
Job A earns more than job B till x = 5, then
Job B will earn more than job A after 5 years (starting from year 6)
Since j
