The mass, \(m\) grams, of a radioactive substance, present at time \(t\) days after first being observed, is given by the formula \(m=28{{\mathrm{e}}^{-0.00072t}}\). Find the value of \(m\) when \(t=20\). Find the value of \(t\) when the mass is half of its value at \(t=0\). State the value which \(m\) approaches as \(t\) becomes very large. Sketch the graph of \(m\) against \(t\).

Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically

The mass, \(m\) grams, of a radioactive substance, present at time \(t\) days after first being observed, is given by the formula \(m=28{{\mathrm{e}}^{-0.00072t}}\).

Find the value of \(m\) when \(t=20\).
Find the value of \(t\) when the mass is half of its value at \(t=0\).
State the value which \(m\) approaches as \(t\) becomes very large.
Sketch the graph of \(m\) against \(t\).

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Answer:(a) \(m=27.6\text{ g}\) (3 s.f.). (b) \(t=963\) days (3 s.f.). (c) \(m\to0\text{ g}\). (d) Decreasing exponential curve through \((0,28)\) with asymptote \(m=0\).

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