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.

Studdy Solution
Compare the populations: - Initially, Calcfield's population grows linearly, while Mathville's grows more slowly. - As time progresses, Mathville's population growth accelerates due to the cubic root function. - The intersection point indicates when both populations are equal, after which Mathville's population surpasses Calcfield's.
The approximate intersection point is calculated to be around t7.2 t \approx 7.2 years after 2000, meaning around the year 2007.2. At this point, both cities have approximately the same population.

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