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f(t)=14(0.85)^(t) The function models f, the value of a professional quality video camera, in thousands of dollars, t years after its purchase. What is the value of the camera at the time of purchase? Choose 1 answer: (A) $11,900 (B) $14,000 (c) $15,000 (D) $85,000

f(t)=14(0.85)t f(t)=14(0.85)^{t} \newlineThe function models f f , the value of a professional quality video camera, in thousands of dollars, t t years after its purchase. What is the value of the camera at the time of purchase?\newlineChoose 11 answer:\newline(A) $11,900 \$ 11,900 \newline(B) $14,000 \$ 14,000 \newline(C) $15,000 \$ 15,000 \newline(D) $85,000 \$ 85,000

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Q. f(t)=14(0.85)t f(t)=14(0.85)^{t} \newlineThe function models f f , the value of a professional quality video camera, in thousands of dollars, t t years after its purchase. What is the value of the camera at the time of purchase?\newlineChoose 11 answer:\newline(A) $11,900 \$ 11,900 \newline(B) $14,000 \$ 14,000 \newline(C) $15,000 \$ 15,000 \newline(D) $85,000 \$ 85,000
  1. Evaluate Function at t=0t=0: To find the value of the camera at the time of purchase, we need to evaluate the function f(t)f(t) at t=0t = 0, because the time of purchase corresponds to the start of the time period, which is year 00.
  2. Substitute t=0t=0 into f(t)f(t): Substitute t=0t = 0 into the function f(t)=14(0.85)tf(t) = 14(0.85)^t to find the initial value.\newlinef(0)=14(0.85)0f(0) = 14(0.85)^0
  3. Calculate f(0)f(0): Recall that any number raised to the power of 00 is 11.$0.85\$0.85^00 = 11\)
  4. Find Value at Purchase: Now, calculate f(0)f(0) using the fact that (0.85)0=1(0.85)^0 = 1.\newlinef(0)=14×1f(0) = 14 \times 1\newlinef(0)=14f(0) = 14
  5. Find Value at Purchase: Now, calculate f(0)f(0) using the fact that (0.85)0=1(0.85)^0 = 1.\newlinef(0)=14×1f(0) = 14 \times 1\newlinef(0)=14f(0) = 14The value of the camera at the time of purchase, f(0)f(0), is 1414 thousand dollars. To express this in dollars, we need to multiply by 1,0001,000.\newlineValue at purchase = 14×1,00014 \times 1,000\newlineValue at purchase = $14,000\$14,000

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