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How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]

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Q. How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
  1. Calculate f(−7)f(-7): We have the function f(t)=−2t−7f(t) = -2t - 7. Calculate the value of f(t)f(t) when t=−7t = -7.
    f(−7)=−2(−7)−7f(-7) = -2(-7) - 7
    f(−7)=14−7f(-7) = 14 - 7
    f(−7)=7f(-7) = 7
  2. Calculate f(−6)f(-6): Calculate the value of f(t)f(t) when t=−6t = -6.
    f(−6)=−2(−6)−7f(-6) = -2(-6) - 7
    f(−6)=12−7f(-6) = 12 - 7
    f(−6)=5f(-6) = 5
  3. Find Change in f: Determine the change in f(t)f(t) over the interval from t=−7t = -7 to t=−6t = -6.
    Change in f(t)f(t) = f(−6)−f(−7)f(-6) - f(-7)
    Change in f(t)f(t) = 5−75 - 7
    Change in f(t)f(t) = −2-2
  4. Analyze Change: Analyze the change in f(t)f(t) to determine if it increases or decreases and by what factor or amount.\newlineSince the change in f(t)f(t) is –2–2, this means f(t)f(t) decreases by 22 as tt increases from –7–7 to –6–6.

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