Answer:
a. f(x) = (122+70x, 0≤x≤5; 62+82x, x>5}
b. f(8) = 718
c. the amount added in 8 weeks
Step-by-step explanation:
a. Reagan's initial balance is 122. He adds 70 per week, so in terms of x weeks, his balance is ...
f(x) = 122 +70x . . . . . for 0 ≤ x ≤ 5
At 5 weeks, his balance is 122 +70·5 = 472. At that point, he adds 70+12 = 82 per week, so the balance will be ...
f(x) = 472 +82(x -5) = 62 +82x . . . . . for x > 5
So, the piecewise function can be defined as ...
[tex]\displaystyle f(x)=\left\{\begin{array}{ll}122+70x&\text{for $0\le x\le 5$}\\62+82x&\text{for $5<x$}\end{array}\right.[/tex]
__
b. f(8) = 62 +82(8) = 718
__
c. f(8) - 122 is the balance after 8 weeks less the initial balance, so represents the amount added to the account in 8 weeks.
