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How does g(x)=6xg(x) = 6^x change over the interval from x=2x = 2 to x=3x = 3?\newlineChoices:\newline(A) g(x)g(x) increases by a factor of 66\newline(B) g(x)g(x) increases by 600%600\%\newline(C) g(x)g(x) decreases by 6%6\%\newline(D) g(x)g(x) increases by 6%6\%

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Q. How does g(x)=6xg(x) = 6^x change over the interval from x=2x = 2 to x=3x = 3?\newlineChoices:\newline(A) g(x)g(x) increases by a factor of 66\newline(B) g(x)g(x) increases by 600%600\%\newline(C) g(x)g(x) decreases by 6%6\%\newline(D) g(x)g(x) increases by 6%6\%
  1. Calculate g(2)g(2): Calculate g(2)g(2) by substituting x=2x = 2 into g(x)=6xg(x) = 6^x.\newlineg(2)=62g(2) = 6^2\newlineg(2)=36g(2) = 36
  2. Calculate g(3)g(3): Now calculate g(3)g(3) by substituting x=3x = 3 into g(x)=6xg(x) = 6^x.
    g(3)=63g(3) = 6^3
    g(3)=216g(3) = 216
  3. Find Change: Find the change from g(2)g(2) to g(3)g(3).\newlineChange = g(3)−g(2)g(3) - g(2)\newlineChange = 216−36216 - 36\newlineChange = 180180
  4. Determine Factor: Determine the factor by which g(x)g(x) increases from x=2x = 2 to x=3x = 3.
    Factor = g(3)g(2)\frac{g(3)}{g(2)}
    Factor = 21636\frac{216}{36}
    Factor = 66

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