Exam 1

  1. Question

    A person takes 400 milligrams of ibuprofen. The amount of ibuprofen in the body tt hours after being administered is given by f(t)=400(0.75)tf(t) = 400 (0.75)^t

    Select each of the true statements from the following:


    1. There is 225 milligrams of ibuprofen in the person’s body 1.5 hours after the ibuprofen was administered.
    2. There is 225 milligrams of ibuprofen in the person’s body 1.5 hours after the ibuprofen was administered.
    3. f(2 hours)=225 milligramsf(2\text{ hours})=225\text{ milligrams}
    4. f(2.5)=259.81f(2.5)=259.81
    5. Using Δx=0.01\Delta x=0.01, the average rate at which ibuprofen is leaving the body 2 hours after administered is -64.64 milligrams per hour.
    6. The instantaneous rate of change of f(t)f(t) with respect to tt at t=2t=2 is f(2+Δt)f(2)Δt \frac{f(2+\Delta t)-f(2)}{\Delta t}

    Solution

    1. False. After 1.5 hours there is 400(0.75)1.5=259.81400(0.75)^1.5=259.81 milligrams of ibuprofen in the person’s body.
    2. False. The amount of ibuprofen in the body 1.5 hours after administered is 400(0.75)1.5=259.81400(0.75)^1.5=259.81.
    3. True. f(2)=4000.752=225f(2)=400\cdot0.75^2=225
    4. False. f(2.5)=400(0.75)2.5=194.86f(2.5)=400(0.75)^2.5=194.86
    5. True. Using Δx=0.01\Delta x=0.01, the average rate at which ibuprofen is leaving the body 2 hours after administered is f(2+0.01)f(2)0.010.646350.0164.64\frac{f(2+0.01)-f(2)}{0.01} \approx \frac{-0.64635}{0.01}\approx-64.64
    6. False. The instantaneous rate of change of f(t)f(t) with respect to tt at t=2t=2 is limΔt0f(2+Δt)f(2)Δt \lim_{\Delta t \rightarrow 0} \frac{f(2+\Delta t)-f(2)}{\Delta t} This is also called the derivative of f(t)f(t) at t=2t=2 and we write f(2)=limΔt0f(2+Δt)f(2)Δt f^'(2)=\lim_{\Delta t \rightarrow 0} \frac{f(2+\Delta t)-f(2)}{\Delta t}