Answer: [tex]C_n=75000(1.05)^n,\text{ for}n\geq0[/tex]
Step-by-step explanation:
Given : Carmela’s annual salary in year n can be modeled by the recursive sequence [tex]C_{n+1} = 1.05 C_n[/tex], where [tex]C_0[/tex] = $75,000.
It is a geometric sequence with common ratio r= 1.05
Explicit formula for geometric sequence:-
[tex]a_n=a_0r^n,\text{ for}n\geq0[/tex]
An explicit formula for a sequence that represents Carmela’s salary will be:
[tex]C_n=C_0(1.05)^n,\text{ for}n\geq0[/tex]
[tex]C_n=75000(1.05)^n,\text{ for}n\geq0[/tex]
