f1.app.edmentum.com TAKE MY Up - Ryne... Can't Ope... (C) ClassLink... (C) CCS Class... (G) in-Googl... Unit Pretest Pretest Select the correct answer. The number of cities in a region over time is represented by the function \( C(x)=2.9(1.05)^{x} \). The approximate number of people per city is represented by the function \( P(x)=(1.05)^{3 x+5} \). Which function best describes \( T(x) \), the approximate population in the region? A. \( \quad T(x)=(6.09)^{4 x+5} \) B. \( \quad T(x)=2.9(1.05)^{4 x+5} \) C. \( \quad T(x)=(3.045)^{x}+(1.05)^{3 x+5} \) D. \( \quad T(x)=2.9(1.05)^{3 x^{2}+5 x} \)

To find the function that best describes \( T(x) \), the approximate population in the region, we need to look at how the number of cities and the population per city interact. Since \( C(x) \) gives the number of cities and \( P(x) \) gives the population per city, we can model the total population as \( T(x) = C(x) \cdot P(x) \). By multiplying the two functions, we have \( T(x) = 2.9(1.05)^x \cdot (1.05)^{3x+5} \), which simplifies to \( T(x) = 2.9(1.05)^{4x+5} \). Therefore, the correct answer is B. Did you know that exponential growth functions like \( C(x) \) and \( P(x) \) are commonly used for modeling populations, bacteria growth, and even financial investments? These functions help predict how a quantity increases over time, making them virtually indispensable in fields ranging from biology to economics! If you're keen to delve deeper into these concepts, start with resources on exponential functions in algebra. Try searching through educational platforms or textbooks that cover functions, growth models, or even calculus. Online lectures or video tutorials can also make these topics more entertaining and engaging!