Collins Mejia
11/09/2023 · High School

There are two functions that can be used to describe the percent of Americans 25 and older who have completed an associate's degree or higher. For both functions \( f(x)=0.72 x+35.2 \) and \( g(x)=0.04 x^{2}+0.47 x+34.9, x \) is the number of years since 2010, and any \( y \) (or \( f(x) \) or \( g(x)) \) is the percent of Americans 25 and older who have completed an associate's degree or higher. Assume that the trend of \( g(x) \) continues. Find \( g(18) \) and describe in words what this means.

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Given the functions: \( f(x) = 0.72x + 35.2 \) \( g(x) = 0.04x^2 + 0.47x + 34.9 \) We are asked to find \( g(18) \) and describe what this means in words. To find \( g(18) \), we substitute \( x = 18 \) into the function \( g(x) \) and calculate the result. Substitute \( x = 18 \) into \( g(x) \): \( g(18) = 0.04(18)^2 + 0.47(18) + 34.9 \) Now, we can calculate \( g(18) \) by evaluating the expression. Calculate the value by following steps: - step0: Calculate: \(0.04\times 18^{2}+0.47\times 18+34.9\) - step1: Multiply the numbers: \(12.96+0.47\times 18+34.9\) - step2: Multiply the numbers: \(12.96+8.46+34.9\) - step3: Add the numbers: \(56.32\) The value of \( g(18) \) is 56.32. This means that in 18 years since 2010, the percent of Americans 25 and older who have completed an associate's degree or higher is approximately 56.32%.

Quick Answer

\( g(18) = 56.32 \). This indicates that in 18 years since 2010, about 56.32% of Americans 25 and older have completed an associate's degree or higher.
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