Respuesta :
Answer:
In the 23rd year his income was of $33,900.
Step-by-step explanation:
Joe's income has been increasing each year by the same dollar amount.
This means that his salary after t years is given by:
[tex]S(t) = S(0) + at[/tex]
In which S(0) is the initial salary and a is the yearly increase.
The first year his income was $22,000
This means that [tex]S(0) = 22000[/tex]. So
[tex]S(t) = S(0) + at[/tex]
[tex]S(t) = 22000 + at[/tex]
In the fourth year his income was $24,100
S(4) = 24100, and thus, we use this to find a.
[tex]S(t) = 22000 + at[/tex]
[tex]24100 = 22000 + 4a[/tex]
[tex]4a = 2100[/tex]
[tex]a = \frac{2100}{4}[/tex]
[tex]a = 525[/tex]
So
[tex]S(t) = 22000 + 525t[/tex]
In which year was his income 33,900
This is t for which S(t) = 33900. So
[tex]S(t) = 22000 + 525t[/tex]
[tex]33900 = 22000 + 525t[/tex]
[tex]525t = 11900[/tex]
[tex]t = \frac{11900}{525}[/tex]
[tex]t = 22.67[/tex]
Rounding up, in the 23rd year his income was of $33,900.
