Subjects algebra

Exponential Growth 4Cfe00

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1. The problem asks us to analyze the exponential function $f(x)$ modeling the population of Center City over time, where $x$ is the number of years after 2015. 2. From the graph, we observe that the population starts near 250,000 at $x=0$ and increases to about 900,000 at $x=100$. 3. Since the graph is increasing and curved upward, the function $f$ is an increasing exponential function. 4. Important properties of exponential functions $f(x) = a \cdot b^x$ with $b>1$ include: - The function is always increasing. - The population grows faster as time increases. - The function never becomes negative. 5. Based on the graph: - The population is increasing over time, so $f$ is increasing. - The growth rate appears to accelerate, so the function is exponential growth, not linear. 6. Therefore, the two true statements are: - The function $f$ is increasing. - The function $f$ models exponential growth of the population over time. Final answer: The function $f$ is increasing and models exponential growth.