After 24 hours, 30% of a 25 milligram dose of a new antibiotic remains in the body. Which of the following functions, M, models the amount of the antibiotic (in milligrams) that remains in the body after h hours? Choose 1 answer: (A) M(h)=30*(0.3)^((h)/( 24)) (B) M(h)=25*(0.3)^((h)/( 24)) (C) M(h)=25*(0.3)^(h) (D) M(h)=25*(0.7)^((h)/( 24))

Question

After 24 hours,  30% of a 25 milligram dose of a new antibiotic remains in the body. Which of the following functions,  M, models the amount of the antibiotic (in milligrams) that remains in the body after  h hours? Choose 1 answer: (A)  M(h)=30*(0.3)^((h)/( 24)) (B)  M(h)=25*(0.3)^((h)/( 24)) (C)  M(h)=25*(0.3)^(h) (D)  M(h)=25*(0.7)^((h)/( 24))

Bytelearn · Accepted Answer

Given Information: We are given that 30% of the antibiotic remains after 24 hours. This means that after 24 hours, the amount of antibiotic left is 30% of the initial dose. We need to find a function that models this decay over time.Initial Dose: The initial dose of the antibiotic is 25 milligrams. We need to express the remaining amount as a function of time, where time is measured in hours (h).Percentage Calculation: Since 30% remains after 24 hours, we can express this as a percentage of the initial dose: 30% of 25 milligrams. To convert the percentage to a decimal, we divide by 100: 30% = 0.3.Exponential Decay Function: The decay of the antibiotic in the body is exponential, and it can be modeled by an exponential decay function. The general form of an exponential decay function is M(h) = initial_amount * (decay_rate)^(time/decay_time).Finding Decay Rate: We need to find the decay rate. After 24 hours, 30% of the antibiotic remains, so the decay rate must be such that when h = 24, the function gives us 30% of the initial dose. This means that the decay rate raised to the power of (24/24) should equal 0.3.Decay Rate Calculation: The decay rate should be such that (decay_rate)^(1) = 0.3. Since raising any number to the power of 1 gives the number itself, the decay rate is 0.3.Writing the Function: Now we can write the function using the initial amount of 25 milligrams and the decay rate of 0.3. The time h will be divided by the period of decay, which is 24 hours, to model the decay over time. This gives us the function M(h) = 25 * (0.3)^(h/24).Matching the Function: Looking at the options provided, option (B) matches the function we derived: M(h) = 25 * (0.3)^(h/24). This function correctly models the amount of the antibiotic that remains in the body after h hours, given that 30% remains after 24 hours.

Full solution

More problems from Volume of cubes and rectangular prisms: word problems

Related topics