# Exam-Style Question on Exponential Models

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 85. This question is similar to one that appeared on 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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