Exam Style Question on Exponential Models
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 85. This question is similar to one that appeared in an IB Studies paper in 2014. The use of a calculator is allowed.
While studying a new disease, scientists found that the number of toxic cells in the bloodstream increased over time, according to the model \(D(t)=12×(1.16)^t , t \ge 0\) where \(D\) is the number of the toxic cells in the bloodstream per litre and \(t\) is the time in hours.
(a) Find the number of toxic cells in the bloodstream at \(t=0\).
(b) Calculate the number of toxic cells in the bloodstream after 3 hours.
(c) Determine the time it takes for the number of toxic cells in the bloodstream to first exceed to 200 per litre. Give your answer to the nearest minute.
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