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How does h(x)=2xh(x) = 2^x change over the interval from x=5x = 5 to x=6x = 6?\newlineChoices:\newline(A) h(x)h(x) increases by 100%100\%\newline(B) h(x)h(x) decreases by 2%2\%\newline(C) h(x)h(x) decreases by 22\newline(D) h(x)h(x) increases by 2%2\%

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Transformations of absolute value functionsright chevron icon

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Q. How does h(x)=2xh(x) = 2^x change over the interval from x=5x = 5 to x=6x = 6?\newlineChoices:\newline(A) h(x)h(x) increases by 100%100\%\newline(B) h(x)h(x) decreases by 2%2\%\newline(C) h(x)h(x) decreases by 22\newline(D) h(x)h(x) increases by 2%2\%
  1. Calculate h(x)h(x): Calculate h(x)h(x) when x=5x = 5.\newlineh(5)=25h(5) = 2^5\newlineh(5)=32h(5) = 32
  2. Calculate h(x)h(x): Calculate h(x)h(x) when x=6x = 6.\newlineh(6)=26h(6) = 2^6\newlineh(6)=64h(6) = 64
  3. Find change in h(x)h(x): Find the change in h(x)h(x) from x=5x = 5 to x=6x = 6.
    Change = h(6)−h(5)h(6) - h(5)
    Change = 64−3264 - 32
    Change = 3232
  4. Calculate percentage increase: Calculate the percentage increase from h(5)h(5) to h(6)h(6).
    Percentage increase = (Change/h(5))×100%(\text{Change} / h(5)) \times 100\%
    Percentage increase = (32/32)×100%(32 / 32) \times 100\%
    Percentage increase = 1×100%1 \times 100\%
    Percentage increase = 100%100\%

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