The amount, $y$ milligrams, of a radioactive isotope present after $t$ years is given by \(y=A{{

Question

The amount, $y$ milligrams, of a radioactive isotope present after $t$ years is given by $y=A{{\mathrm e}^{-0.3t}}$, where $A$ is a constant. At the beginning, there was an initial amount of $300$mg. Find the value of $A$, the amount present after $5$ years, the year in which the amount of substance would be expected to be halved, the amount that has decayed after $3$ years.

Accepted Answer

(a) $A=300$ (b) $66.9\text{ mg}$ (c) During the third year, at approximately $2.31$ years (d) $178\text{ mg}$ (3 s.f.).

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

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