Question

Reagan had $122 in savings account. He deposited $70 each week from his job for the first 5 weeks of summer. In the sixth week, Reagan got a raise and increased his weekly deposits by $12.​

Answer 1

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 ...

  $\displaystyle f(x)=\left\{\begin{array}{ll}122+70x&\text{for 0\le x\le 5 }\\62+82x&\text{for 5<x }\end{array}\right.$

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b. f(8) = 62 +82(8) = 718

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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.