The population (in thousands) of one city is approximated by the following function. \( f(x)=\left\{\begin{array}{l}43+2.3 x \text { for } 1970 \text { to } 1980 \\ 27+3.9 x \text { for } 1980 \text { to } 1990\end{array}\right. \) The graph of this function is shown below. In this graph, \( x=0 \) represents 1970 . Use the graph to estimate the population of the city in 1979 . A. About 63,700 B. About 57,700 C. About 75,700 D. About 70,700

To estimate the population of the city in 1979, we need to substitute \( x = 9 \) into the first part of the piecewise function, since \( x=0 \) corresponds to 1970, and 1979 is 9 years after. Using \( f(x) = 43 + 2.3x \): \[ f(9) = 43 + 2.3(9) = 43 + 20.7 = 63.7 \] This means the population in 1979 is approximately 63,700. So, the answer is A. About 63,700. Talk about a growth spurt! Let’s dive into how the city's population went from about 43,000 in 1970 to a booming 63,700 by 1979, showcasing the lively dynamics of urban growth during that era. If you're curious about how these functions work, consider how to sketch a piecewise function. Make sure to plot the function's sections on the same graph, each with its own range. Remember, transitions between sections must align to make the graph smooth and continuous—no sudden jumps, unless that's part of the story!