# Science:Math Exam Resources/Courses/MATH110/December 2016/Question 09 (a)

MATH110 December 2016
Other MATH110 Exams

### Question 09 (a)

Sugar dissolves in water at a rate proportional to the amount still undissolved.

Suppose the amount $M$ of undissolved sugar present in a water solution $t$ hours after the sugar was added to the water is modelled using an exponential decay function $M(t)=Ce^{-kt}$ , where $C$ and $k$ are positive constants. Suppose initially $10{\text{ kg}}$ of sugar are added to the water. Assume it takes $4{\text{ hr}}$ for half of the initial amount of sugar to dissolve. Answer the questions below. You may leave your answers unsimplified, i.e. in ”calculator-ready” form.

(a) Find the exponential function that predicts the amount of undissolved sugar $M(t)$ present in the solution at $t{\text{ hr}}$ . Make sure your answer has no unknown constants.

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