Olivia has taken an initial dose of a prescription medication. The relationship between the elapsed time t, in hours, since she took the first dose, and the amount of medication M(t), in milligrams ( mg ), remaining in her bloodstream is modeled by the following function. M(t)=50*e^(-0.75 t) How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours? Round your answer, if necessary, to the nearest hundredth. mg

Question

Olivia has taken an initial dose of a prescription medication. The relationship between the elapsed time  t, in hours, since she took the first dose, and the amount of medication  M(t), in milligrams (  mg ), remaining in her bloodstream is modeled by the following function.  M(t)=50*e^(-0.75 t) How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours? Round your answer, if necessary, to the nearest hundredth. mg

Bytelearn · Accepted Answer

Identify function and time: Identify the given function and the time at which we need to find the amount of medication. The function given is M(t) = 50 * e^(-0.75t), and we need to find M(6).Substitute value of t: Substitute the value of t with 6 hours into the function. M(6) = 50 * e^(-0.75 * 6)Calculate exponent: Calculate the exponent part of the function. -0.75 * 6 = -4.5Calculate value of e: Calculate the value of e raised to the power of -4.5. e^(-4.5) ≈ 0.011109Multiply by 50: Multiply the result from Step 4 by 50 to find the amount of medication remaining. M(6) = 50 * 0.011109Perform multiplication: Perform the multiplication to get the final result. M(6) ≈ 50 * 0.011109 ≈ 0.55545Round to nearest hundredth: Round the result to the nearest hundredth. M(6) ≈ 0.56 mg

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