## Exam-Style Question on Exponential Models## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 373. This question is similar to one that appeared on an IB Standard paper in 2019. The use of a calculator is allowed.

Fifty milligrams of a certain type of medicine has been shown to enter the bloodstream of an adult according to the following equations:

- Rate of entry, \(R = 8 \times 0.93^t \) mg/min
- Amount in bloodstream, \(A = 49(1 - 0.44)^t \) mg

where \(t\) is measured in minutes and \( t\ge 0 \)

(a) State the initial rate at which the medicine enters the bloodstream.

(b) Calculate the time it takes before the rate at which the medicine enters the bloodstream is halved.

(c) Find the rate of the medicine entering the bloodstream when there is 25 mg present in the bloodstream.

(d) Sketch both R and A on the same axes. Indicate clearly any intercepts and the equations of the horizontal asymptotes.

(e) Will the patient ever feel the full effect of the 50-milligram dose?

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