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How does f(t)=2tf(t) = 2^t change over the interval from t=1t = 1 to t=2t = 2?\newlineChoices:\newline(A) f(t)f(t) decreases by 2%2\%\newline(B) f(t)f(t) increases by 200%200\%\newline(C) f(t)f(t) increases by a factor of 22\newline(D) f(t)f(t) increases by 22

Full solution

Q. How does f(t)=2tf(t) = 2^t change over the interval from t=1t = 1 to t=2t = 2?\newlineChoices:\newline(A) f(t)f(t) decreases by 2%2\%\newline(B) f(t)f(t) increases by 200%200\%\newline(C) f(t)f(t) increases by a factor of 22\newline(D) f(t)f(t) increases by 22
  1. Calculate f(t)f(t): Calculate f(t)f(t) when t=1t = 1.\newlinef(1)=21=2f(1) = 2^1 = 2.
  2. Calculate f(t)f(t): Calculate f(t)f(t) when t=2t = 2.\newlinef(2)=22=4f(2) = 2^2 = 4.
  3. Compare values: Compare f(2)f(2) to f(1)f(1) to find the change.\newlineThe change is 42=24 - 2 = 2.
  4. Determine percentage increase: Determine the percentage increase from f(1)f(1) to f(2)f(2).\newlinePercentage increase = ChangeOriginal value×100%=22×100%=100%\frac{\text{Change}}{\text{Original value}} \times 100\% = \frac{2}{2} \times 100\% = 100\%.

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