Questions: The number of students (in thousands) of osteopathic medicine in a country can be described by 0.027t^2 - 4.75t + 226.72, where t is the number of years after 1990. Use a graphing utility to graph this function on the viewing window [0,17] by [0,300]. Use the graphing utility to predict the number of students of osteopathic medicine in the country in 2006.

The number of students (in thousands) of osteopathic medicine in a country can be described by 0.027t^2 - 4.75t + 226.72, where t is the number of years after 1990. Use a graphing utility to graph this function on the viewing window [0,17] by [0,300]. Use the graphing utility to predict the number of students of osteopathic medicine in the country in 2006.
Transcript text: number of students (in thousands) of osteopathic medicine in a country can be described by $0.027 t^{2}-4.75 t+226.72$, where $t$ is the number of years after 1990 Use a graphing utility to graph this function on the viewing window $[0,17]$ by $[0,300]$ Use the graphing utility to predict the number of students of osteopathic medicine in the country in 2006.
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Solution

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Solution Steps

Step 1: Define the function for the number of students

The function describing the number of students (in thousands) of osteopathic medicine is given by: \[ f(t) = 0.027 t^{2} - 4.75 t + 226.72 \]

Step 2: Determine the year 2006 in terms of \( t \)

Since \( t \) is the number of years after 1990, for the year 2006: \[ t = 2006 - 1990 = 16 \]

Step 3: Calculate the number of students in 2006

Substitute \( t = 16 \) into the function: \[ f(16) = 0.027 \times 16^{2} - 4.75 \times 16 + 226.72 \]

Calculate: \[ f(16) = 0.027 \times 256 - 4.75 \times 16 + 226.72 \] \[ f(16) = 6.912 - 76 + 226.72 \] \[ f(16) = 157.632 \]

Final Answer

The predicted number of students of osteopathic medicine in the country in 2006 is approximately 157.632 thousand.

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