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$f(t) = 14(0.85)^t$ $\newline$ 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? $\newline$ Choose $1$ answer: $\newline$ (A) $\$11,900$ $\newline$ (B) $\$14,000$ $\newline$ (C) $\$15,000$ $\newline$ (D) $\$85,000$

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Find derivatives of inverse trigonometric functions

Full solution

Q.

f(t) = 14(0.85)^t

\newline

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?

\newline

Choose

1

answer:

\newline

(A)

\$11,900

\newline

(B)

\$14,000

\newline

(C)

\$15,000

\newline

(D)

\$85,000

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. $\newline$ $f(0) = 14(0.85)^0$
Calculate $f(0)$ : Any non-zero number raised to the power of $0$ is $1$ . Therefore, $(0.85)^0 = 1$ . $\newline$ $f(0) = 14 \times 1$
Multiply to find value: Multiply $14$ by $1$ to get the value of the camera at the time of purchase. $\newline$ $f(0) = 14$
Convert 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 $1,000$ . $\newline$ Value at purchase = $14 \times 1,000 = \$(14,000)$

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