Math  /  Algebra

QuestionBetween 2000 and 2020, the population of Mathville could be modeled by the function m(t)=100t3m(t)=100 \sqrt[3]{t}, where m(t)m(t) is the number of people in Mathville, and tt is the number of years since 2000. Between those same years, the population of Calcfield could be modeled by the function c(t)=18tc(t)=18 t. A. Graph each function on graph paper or a neatly made coordinate grid by hand. Be sure to consider an appropriate domain for the functions as you make your graph. B. Approximately where do the functions intersect? What does this point of intersection represent? C. Write and solve an equation to algebraically confirm where the two functions intersect. Show your work. D. Write 2-3 complete sentences comparing the relative populations of the cities over time (10 points)

Studdy Solution
The intersection point represents the year when the populations of Mathville and Calcfield are equal. This occurs approximately 13 years after 2000, which is around the year 2013.
Compare the populations over time:
Initially, Calcfield's population grows linearly, while Mathville's population grows at a decreasing rate due to the cube root. By around 2013, both populations are equal. After this point, Calcfield's population continues to grow faster than Mathville's.
The functions intersect at approximately t13.12 t \approx 13.12 , representing the year 2013. At this point, both cities have the same population.

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