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Wyatt put the $450 she earned from her summer job into an account and will use it to pay for school expenses. She withdraws 10% of the remaining balance each month to pay for part of her living expenses. Which of the following functions models the balance, B, of Wyatt's money (in dollars) t months after she started school? Choose 1 answer: (A) B(t)=450*(1.1)^(t) (B) B(t)=450*(0.9)^(t) (c) B(t)=450+1.1 t (D) B(t)=450-0.9 t

Wyatt put the $450 \$ 450 she earned from her summer job into an account and will use it to pay for school expenses. She withdraws 10% 10 \% of the remaining balance each month to pay for part of her living expenses. Which of the following functions models the balance, B B , of Wyatt's money (in dollars) t t months after she started school?\newlineChoose 11 answer:\newline(A) B(t)=450⋅(1.1)t B(t)=450 \cdot(1.1)^{t} \newline(B) B(t)=450⋅(0.9)t B(t)=450 \cdot(0.9)^{t} \newline(C) B(t)=450+1.1t B(t)=450+1.1 t \newline(D) B(t)=450−0.9t B(t)=450-0.9 t

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Q. Wyatt put the $450 \$ 450 she earned from her summer job into an account and will use it to pay for school expenses. She withdraws 10% 10 \% of the remaining balance each month to pay for part of her living expenses. Which of the following functions models the balance, B B , of Wyatt's money (in dollars) t t months after she started school?\newlineChoose 11 answer:\newline(A) B(t)=450⋅(1.1)t B(t)=450 \cdot(1.1)^{t} \newline(B) B(t)=450⋅(0.9)t B(t)=450 \cdot(0.9)^{t} \newline(C) B(t)=450+1.1t B(t)=450+1.1 t \newline(D) B(t)=450−0.9t B(t)=450-0.9 t
  1. Problem Understanding: Understand the problem.\newlineWyatt withdraws 10%10\% of the remaining balance each month. This means that each month, she has 90%90\% of the previous month's balance left.
  2. Mathematical Model: Translate the situation into a mathematical model.\newlineSince Wyatt withdraws 10%10\% each month, the balance is multiplied by 0.90.9 each month. This is a geometric sequence where each term is 0.90.9 times the previous term, starting with 450450.
  3. Identifying the Function: Identify the correct function.\newlineThe function that models a quantity that decreases by a constant percentage over time is an exponential decay function. The general form of such a function is B(t)=B0⋅(1−r)tB(t) = B_0 \cdot (1 - r)^t, where B0B_0 is the initial amount, rr is the decay rate, and tt is time.
  4. Matching the Situation: Match the situation with the given options.\newlineThe correct function must have an initial amount of 450450 and a decay rate of 10%10\%, which is 0.10.1. Therefore, the function should be B(t)=450×(1−0.1)t=450×(0.9)tB(t) = 450 \times (1 - 0.1)^t = 450 \times (0.9)^t.
  5. Choosing the Answer: Choose the correct answer.\newlineThe function that matches our model is B(t)=450×(0.9)tB(t) = 450 \times (0.9)^t, which is option (B)(B).

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