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At the moment a certain medicine is injected, its concentration in the bloodstream is 120 milligrams per liter. From that moment forward, the medicine's concentration drops by 
30% each hour.
Write a function that gives the medicine's concentration in milligrams per liter, 
C(t),t hours after the medicine was injected.

C(t)=◻++^(x)

At the moment a certain medicine is injected, its concentration in the bloodstream is 120120 milligrams per liter. From that moment forward, the medicine's concentration drops by 30% 30 \% each hour.\newlineWrite a function that gives the medicine's concentration in milligrams per liter, C(t) C(t) , t t hours after the medicine was injected.\newlineC(t)= C(t)=\square

Full solution

Q. At the moment a certain medicine is injected, its concentration in the bloodstream is 120120 milligrams per liter. From that moment forward, the medicine's concentration drops by 30% 30 \% each hour.\newlineWrite a function that gives the medicine's concentration in milligrams per liter, C(t) C(t) , t t hours after the medicine was injected.\newlineC(t)= C(t)=\square
  1. Identify initial concentration and rate: Step 11: Identify the initial concentration and the rate of decrease. The initial concentration is given as 120120 milligrams per liter. The concentration decreases by 30%30\% each hour, which means that 70%70\% of the concentration remains each hour.
  2. Convert percentage to decimal form: Step 22: Convert the percentage that remains each hour into decimal form to use as the base of the exponential function. Since 70%70\% remains, the decimal equivalent is 0.700.70.
  3. Write exponential decay function: Step 33: Write the exponential decay function. The general form of an exponential decay function is C(t)=C0×btC(t) = C_0 \times b^t, where C0C_0 is the initial concentration and bb is the base representing the hourly decrease. In this case, C0=120C_0 = 120 and b=0.70b = 0.70.
  4. Substitute values into function: Step 44: Substitute the values into the exponential decay function to get the specific function for this situation. C(t)=120×0.70tC(t) = 120 \times 0.70^t.
  5. Verify function accuracy: Step 55: Verify that the function correctly represents the situation. At t=0t = 0 (the moment the medicine is injected), C(0)=120×0.700=120×1=120C(0) = 120 \times 0.70^0 = 120 \times 1 = 120 milligrams per liter, which matches the initial condition.

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