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)=□
Q. 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)=□
Identify initial concentration and rate: Step 1: Identify the initial concentration and the rate of decrease. The initial concentration is given as 120 milligrams per liter. The concentration decreases by 30% each hour, which means that 70% of the concentration remains each hour.
Convert percentage to decimal form: Step 2: Convert the percentage that remains each hour into decimal form to use as the base of the exponential function. Since 70% remains, the decimal equivalent is 0.70.
Write exponential decay function: Step 3: Write the exponential decay function. The general form of an exponential decay function is C(t)=C0×bt, where C0 is the initial concentration and b is the base representing the hourly decrease. In this case, C0=120 and b=0.70.
Substitute values into function: Step 4: Substitute the values into the exponential decay function to get the specific function for this situation. C(t)=120×0.70t.
Verify function accuracy: Step 5: Verify that the function correctly represents the situation. At t=0 (the moment the medicine is injected), C(0)=120×0.700=120×1=120 milligrams per liter, which matches the initial condition.
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