(7) An employee joined a company in 2017 with a starting salary of 50000 USD. Every year this employee receives a raise of 1000 USD plus 5 percent of the salary of the previous year. Let Cn denote the employee's salary n years after 2017. (a) Set up a recurrence relation for Cn. (b) What will the salary of this employee be in 2025? (c) Find an explicit formula for Cn.

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C0=50 000

a.)Cn=Cn-1*1.05 + 1 000

b.)C1=53 500

C2=57 175

C3=61 033.75

C4=65 085.4375

C5=69 339.7094

C6=73 806.6949

C7=78 497.0296

C2025-2017=C8=83 421.8811

c.) $C=50000$

$k= 1 + 5/100$

$d=1000$

$C$ 1 $=C*k+d,$

$C$ 2 $=C$ 1 $*k+d=C*k^2+d*k+d$ $=$

$C*k^2+d*(k+1),$

$C$ 3 $=C*k^3+d*(k^2+k+1),$

$C_4$ $=C*k^4+d*(k^3+k^2+k+1),$

$\sum_{i=0}^{n-1} k^i=(k^n-1)/(k-1),$

Cn $=C*k^n+d*(k^n-1)/(k-1)=50000*1.05^n+1000*(1.05^n-1)/0.05$