Dunn Barker
05/02/2024 · Junior High School
In this exercise we use a graphing device to compare the rates of growth of the graphs of a power function and an exponential function. Compare the rates of growth of the functions \( f(x)=3^{x} \) and \( g(x)=x^{4} \) by drawing the graphs of both functions in the following viewing rectangles. (i) \( [-4,4] \) by \( [0,20] \) (ii) \( [0,10] \) by \( [0,5000] \) (iii) \( [0,20] \) by \( \left[0,10^{5}\right] \) Find the solutions of the equation \( 3^{x}=x^{4} \), rounded to two decimal places. (Enter your answers as a comma-separated list.) \( x=\square \)
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The solutions to \( 3^x = x^4 \) are approximately \( x = 0.77 \) and \( x = 3.56 \).
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