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The radioactive decay of a substance is given by

1000e^{-ct}, \quad t \geq 0.

where $R\,$ is the number of atoms at time $t\,$ years and $c\,$ is a positive constant.

a.

Find the number of atoms when the substance started to decay.

[1]

b.

It takes 5730 years for half of the substance to decay. Find the value of $c\,$ to 3 significant figures.

[4]

c.

Calculate the number of atoms that will be left when $t = 22, 920$ .

[2]

d.

Sketch the graph of $R\,$ against $t$ .

[2]

Logs

The radioactive decay of a substance is given by

1000e^{-ct}, \quad t \geq 0.

where $R\,$ is the number of atoms at time $t\,$ years and $c\,$ is a positive constant.

a.

Find the number of atoms when the substance started to decay.

[1]

b.

It takes 5730 years for half of the substance to decay. Find the value of $c\,$ to 3 significant figures.

[4]

c.

Calculate the number of atoms that will be left when $t = 22, 920$ .

[2]

d.

Sketch the graph of $R\,$ against $t$ .

[2]

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Logs Questions