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How does f(t)=2tf(t) = 2^t change over the interval from t=5t = 5 to t=6t = 6?\newlineChoices:\newline(A) f(t)f(t) increases by a factor of 22\newline(B) f(t)f(t) decreases by a factor of 22\newline(C) f(t)f(t) increases by 200%200\%\newline(D) f(t)f(t) increases by 22

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Q. How does f(t)=2tf(t) = 2^t change over the interval from t=5t = 5 to t=6t = 6?\newlineChoices:\newline(A) f(t)f(t) increases by a factor of 22\newline(B) f(t)f(t) decreases by a factor of 22\newline(C) f(t)f(t) increases by 200%200\%\newline(D) f(t)f(t) increases by 22
  1. Calculate f(t)f(t) at t=5t=5: Calculate f(t)f(t) when t=5t = 5.\newlinef(5)=25f(5) = 2^5\newlinef(5)=32f(5) = 32
  2. Calculate f(t)f(t) at t=6t=6: Calculate f(t)f(t) when t=6t = 6.\newlinef(6)=26f(6) = 2^6\newlinef(6)=64f(6) = 64
  3. Find change in f(t)f(t): Find the change in f(t)f(t) from t=5t = 5 to t=6t = 6.\newlineChange = f(6)f(5)f(6) - f(5)\newlineChange = 643264 - 32\newlineChange = 3232
  4. Determine factor of increase: Determine the factor by which f(t)f(t) increases.\newlineFactor = f(6)f(5)\frac{f(6)}{f(5)}\newlineFactor = 6432\frac{64}{32}\newlineFactor = 22

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