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The administrators of a factory modeled the cumulative average construction time in minutes per engine component as a function of the total number of components their employees had previously constructed,
n, using the following function:

T(n)=3.5+7*0.9^(n)
What was the cumulative average time, in minutes, for an employee to construct one engine component when they first began?

The administrators of a factory modeled the cumulative average construction time in minutes per engine component as a function of the total number of components their employees had previously constructed, $n$ , using the following function: $\newline$ $T(n)=3.5+7 \cdot 0.9^{n}$ $\newline$ What was the cumulative average time, in minutes, for an employee to construct one engine component when they first began?

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Write linear functions: word problems

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Q. The administrators of a factory modeled the cumulative average construction time in minutes per engine component as a function of the total number of components their employees had previously constructed,

n

, using the following function:

\newline

T(n)=3.5+7 \cdot 0.9^{n}

\newline

What was the cumulative average time, in minutes, for an employee to construct one engine component when they first began?

Identify function and value of $n$ : Identify the given function and the value of $n$ when the employee first began constructing engine components. $\newline$ The function is $T(n) = 3.5 + 7 \times 0.9^{(n)}$ . When the employee first began, they had constructed $0$ components, so $n = 0$ .
Substitute $n = 0$ into function: Substitute $n = 0$ into the function to find the cumulative average time for the first engine component. $T(0) = 3.5 + 7 \times 0.9^{(0)}$ Since any number to the power of $0$ is $1$ , $0.9^{(0)} = 1$ .
Calculate cumulative average time: Calculate the cumulative average time using the substituted values. $\newline$ $T(0) = 3.5 + 7 \times 1$ $\newline$ $T(0) = 3.5 + 7$ $\newline$ $T(0) = 10.5$ $\newline$ The cumulative average time for an employee to construct one engine component when they first began is $10.5$ minutes.

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