Maleko is mayor of a growing town with many job opportunities. He has observed a growing rise in his town's population over the past two years. Each month there are 10% more people. Maleko would like to predict the population of the town in 10 months from now.Which type of trendline would be the best choice to model the relationship between months and population?Group of answer choicesLinearExponentialThere will not be a predictable relationship between the two variables.Quadratic
Question
Maleko is mayor of a growing town with many job opportunities. He has observed a growing rise in his town's population over the past two years. Each month there are 10% more people. Maleko would like to predict the population of the town in 10 months from now.Which type of trendline would be the best choice to model the relationship between months and population?Group of answer choicesLinearExponentialThere will not be a predictable relationship between the two variables.Quadratic
Solution
Para responder a la pregunta sobre qué tipo de línea de tendencia sería la mejor para modelar la relación entre los meses y la población, sigamos los siguientes pasos:
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Entender el crecimiento observado: Maleko ha observado que cada mes hay un 10% más de personas en la población. Esto indica un crecimiento porcentual constante.
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Identificar el tipo de crecimiento: Un crecimiento porcentual constante es característico de un crecimiento exponencial. En un crecimiento exponencial, la cantidad aumenta por un factor constante en cada período de tiempo.
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Comparar con otros tipos de tendencias:
- Lineal: Un crecimiento lineal implica un aumento constante en términos absolutos (por ejemplo, 100 personas más cada mes), no en términos porcentuales.
- Cuadrática: Un crecimiento cuadrático implica que la tasa de crecimiento cambia de manera que la relación entre las variables se puede describir con una ecuación de segundo grado.
- No predecible: La observación de un aumento constante del 10% cada mes sugiere que hay una relación predecible entre los meses y la población.
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Conclusión: Dado que la población aumenta en un 10% cada mes, la mejor opción para modelar esta relación es una tendencia exponencial.
Por lo tanto, la respuesta correcta es Exponential.
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