Questions: The bar graph shows the average temperature for a certain city, in degrees Fahrenheit, for seven selected years The data can be modeled by the linear function f(x)=0.019 x+56.65, where f(x) is the average temperature, in degrees Fahrenheit, x years after 1900. The graph of f is shown to the right. Complete parts (a) through (b). a. Find and interpret f(80). Use the equation for f(x) to identify this information as a point on the graph. The point is (80,58.17) (Type an ordered pair.) Interpret this information. The average temperature in the city in the year was degrees F.

The bar graph shows the average temperature for a certain city, in degrees Fahrenheit, for seven selected years The data can be modeled by the linear function f(x)=0.019 x+56.65, where f(x) is the average temperature, in degrees Fahrenheit, x years after 1900. The graph of f is shown to the right. Complete parts (a) through (b). a. Find and interpret f(80). Use the equation for f(x) to identify this information as a point on the graph. The point is (80,58.17) (Type an ordered pair.) Interpret this information. The average temperature in the city in the year was degrees F.
Transcript text: The bar graph shows the average temperature for a certain city, in degrees Fahrenheit, for seven selected years The data can be modeled by the linear function $f(x)=0.019 x+56.65$, where $f(x)$ is the average temperature, in degrees Fahrenheit, $x$ years after 1900. The graph of f is shown to the right. Complete parts (a) through (b). a. Find and interpret $f(80)$. Use the equation for $f(x)$ to identify this information as a point on the graph. The point is $(80,58.17)$ (Type an ordered pair.) Interpret this information. The average temperature in the city in the year $\square$ was $\square$ ${ }^{\circ} \mathrm{F}$.
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Solution

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Solution Steps

Step 1: Identify the given function and the value to be evaluated

The given linear function is \( f(x) = 0.019x + 56.65 \), where \( f(x) \) represents the average temperature in degrees Fahrenheit, and \( x \) is the number of years after 1900. We need to find \( f(80) \).

Step 2: Substitute the value into the function

Substitute \( x = 80 \) into the function: \[ f(80) = 0.019(80) + 56.65 \]

Step 3: Perform the calculation

Calculate the value: \[ f(80) = 0.019 \times 80 + 56.65 \] \[ f(80) = 1.52 + 56.65 \] \[ f(80) = 58.17 \]

Final Answer

The average temperature in the city in the year 1980 (80 years after 1900) was \( 58.17^\circ \text{F} \).

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