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

Question

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

Bytelearn · Accepted Answer

Evaluate Function at t=0: To find the value of the camera at the time of purchase, we need to evaluate the function f(t) at t = 0, because the time of purchase corresponds to the start of the time period, which is t = 0.Substitute t=0 into f(t): Substitute t = 0 into the function f(t) = 14(0.85)^t to find the initial value. f(0) = 14(0.85)^0Calculate f(0): Any non-zero number raised to the power of 0 is 1. Therefore, (0.85)^0 = 1. f(0) = 14 * 1Multiply to find value: Multiply 14 by 1 to get the value of the camera at the time of purchase. f(0) = 14Convert to actual dollars: The value of the camera at the time of purchase is 14 thousand dollars. Since the value is given in thousands of dollars, we need to convert it to actual dollars by multiplying by 1,000. Value at purchase = 14 * 1,000 = $14,000

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