An efficiency expert hired by a manufacturing firm has compiled the following data relating workers' output to their experience: $Q ( t ) = 600 - A e ^ { - k t }$ Experience (months) 0 9 Output (units per hour) 200 580 The expert believes that the output Q is related to experience t by a function of the form. Find the function of this form that fits the data. Round numbers to four decimal places, if necessary.
A) $Q ( t ) = 600 - 400 e ^ { 0.3329 t }$
B) $Q ( t ) = 600 - 400 e ^ { - 0.3329 t }$
C) $Q ( t ) = 600 - 580 e ^ { 0.3329 t }$
D) $Q ( t ) = 600 - 580 e ^ { - 0.3329 t }$

Question

Quizplus · Accepted Answer

Given the function $Q(t) = 600 - A e^{-kt}$, we need to find the values of $A$ and $k$ that fit the provided data points: at $t = 0$, $Q(t) = 200$, and at $t = 9$, $Q(t) = 580$.1. For $t = 0$, $Q(0) = 600 - A e^{0} = 200$. Solving for $A$, we find $A = 400$.2. For $t = 9$, $Q(9) = 600 - 400 e^{-k(9)} = 580$. Solving for $k$, we find $k \approx 0.3329$.Therefore, the correct function is $Q(t) = 600 - 400 e^{-0.3329t}$.

An Efficiency Expert Hired by a Manufacturing Firm Has Compiled Q(t)=600−Ae−ktQ ( t ) = 600 - A e ^ { - k t }Q(t)=600−Ae−kt

An Efficiency Expert Hired by a Manufacturing Firm Has Compiled $Q ( t ) = 600 - A e ^ { - k t }$