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How does h(x)=5xh(x) = 5^x change over the interval from x=8x = 8 to x=9x = 9?\newlineChoices:\newline(A) h(x)h(x) increases by 400%400\%\newline(B) h(x)h(x) increases by 55\newline(C) h(x)h(x) increases by 500%500\%\newline(D) h(x)h(x) decreases by 55

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Q. How does h(x)=5xh(x) = 5^x change over the interval from x=8x = 8 to x=9x = 9?\newlineChoices:\newline(A) h(x)h(x) increases by 400%400\%\newline(B) h(x)h(x) increases by 55\newline(C) h(x)h(x) increases by 500%500\%\newline(D) h(x)h(x) decreases by 55
  1. Calculate h(x)h(x): Calculate h(x)h(x) when x=8x = 8.\newlineh(8)=58h(8) = 5^8
  2. Calculate h(x)h(x): Calculate h(x)h(x) when x=9x = 9.\newlineh(9)=59h(9) = 5^9
  3. Find increase: Find the increase from h(8)h(8) to h(9)h(9).\newlineIncrease = h(9)−h(8)=59−58h(9) - h(8) = 5^9 - 5^8
  4. Factor out 585^8: Factor out 585^8 to simplify the calculation.\newlineIncrease = 58×(5−1)=58×45^8 \times (5 - 1) = 5^8 \times 4
  5. Calculate percentage increase: Calculate the percentage increase.\newlinePercentage increase = (Increaseh(8))×100%(\frac{\text{Increase}}{h(8)}) \times 100\% = (58×458)×100%(\frac{5^8 \times 4}{5^8}) \times 100\%
  6. Simplify percentage increase: Simplify the percentage increase calculation.\newlinePercentage increase = 4×100%=400%4 \times 100\% = 400\%

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