Questions: The bar graph shows the average atmospheric concentration of a pollutant in ppm for seven selected years. The data can be modeled by the functions f(x)=1.27x+310 and g(x)=0.01x^2+0.6x+313 where f(x) and g(x) represent the average concentration of pollutant in ppm x years after 1950. Complete parts (a) through (c). a. Find and interpret f(40). Use the equation for f(x) to identify this information as a point on the graph. (Type an ordered pair.)

The bar graph shows the average atmospheric concentration of a pollutant in ppm for seven selected years.

The data can be modeled by the functions f(x)=1.27x+310 and g(x)=0.01x^2+0.6x+313 where f(x) and g(x) represent the average concentration of pollutant in ppm x years after 1950. Complete parts (a) through (c).
a. Find and interpret f(40). Use the equation for f(x) to identify this information as a point on the graph.
(Type an ordered pair.)
Transcript text: The bar graph shows the average atmospheric concentration of a pollutant in ppm for seven selected years. The data can be modeled by the functions $f(x)=1.27 x+310$ and $g(x)=0.01 x^{2}+0.6 x+313$ where $f(x)$ and $g(x)$ represent the average concentration of pollutant in $\mathrm{ppm} x$ years after 1950. Complete parts (a) through (c). a. Find and interpret $\mathrm{f}(40)$. Use the equation for $\mathrm{f}(\mathrm{x})$ to identify this information as a point on the graph. $\square$ (Type an ordered pair.)
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Solution

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Solution Steps

Step 1: Identify the function f(x)

The function given is \( f(x) = 1.27x + 310 \). This function models the average concentration of the pollutant in ppm \( x \) years after 1950.

Step 2: Substitute x = 40 into f(x)

To find \( f(40) \), substitute \( x = 40 \) into the function: \[ f(40) = 1.27(40) + 310 \]

Step 3: Calculate the value of f(40)

Perform the calculation: \[ f(40) = 1.27 \times 40 + 310 \] \[ f(40) = 50.8 + 310 \] \[ f(40) = 360.8 \]

Final Answer

The value of \( f(40) \) is 360.8. The point on the graph is (40, 360.8).

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