The mass, $m$ grams, of a radioactive substance is given by the formula $m=m_0{\mathrm{e}}^{-kt}$, where $t$ is the time in days after the mass was first recorded and $m_0$ and $k$ are constants.

The table below shows experimental values of $t$ and $m$.

$t$	$10$	$20$	$30$	$40$	$50$
$m$	$40.9$	$33.5$	$27.4$	$22.5$	$18.4$

Draw the graph of $\ln m$ against $t$.

The mass, $m$ grams, of a radioactive substance is given by the formula $m=m_0{\mathrm{e}}^{-kt}$, where $t$ is the time in days after the mass was first recorded and $m_0$ and $k$ are constants.

The table below shows experimental values of $t$ and $m$.

Use your graph to estimate the value of $m_0$ and $k$.

The mass, $m$ grams, of a radioactive substance is given by the formula $m=m_0{\mathrm{e}}^{-kt}$, where $t$ is the time in days after the mass was first recorded and $m_0$ and $k$ are constants.

The table below shows experimental values of $t$ and $m$.

The half-life of a radioactive substance is the time it takes to decay to half of its original mass. Find the half-life of this radioactive substance.

The temperature, $T°\mathrm{C}$, of a hot drink, $t$ minutes after it is made, can be modelled by the equation $T=25+k{\mathrm{e}}^{-nt}$, where $k$ and $n$ are constants. The table below shows experimental values of $t$ and $T$.

Convert the equation to a form suitable for drawing a straight-line graph.

The temperature, $T°\mathrm{C}$, of a hot drink, $t$ minutes after it is made, can be modelled by the equation $T=25+k{\mathrm{e}}^{-nt}$, where $k$ and $n$ are constants. The table below shows experimental values of $t$ and $T$.

Draw the straight-line graph and use it to estimate the value of $k$ and $n .$

The temperature, $T°\mathrm{C}$, of a hot drink, $t$ minutes after it is made, can be modelled by the equation $T=25+k{\mathrm{e}}^{-nt}$, where $k$ and $n$ are constants. The table below shows experimental values of $t$ and $T$.

Estimate:

the initial temperature of the drink

The temperature, $T°\mathrm{C}$, of a hot drink, $t$ minutes after it is made, can be modelled by the equation $T=25+k{\mathrm{e}}^{-nt}$, where $k$ and $n$ are constants. The table below shows experimental values of $t$ and $T$.

Estimate:

the time taken for the temperature to reach $28°\mathrm{C}$

The temperature, $T°\mathrm{C}$, of a hot drink, $t$ minutes after it is made, can be modelled by the equation $T=25+k{\mathrm{e}}^{-nt}$, where $k$ and $n$ are constants. The table below shows experimental values of $t$ and $T$.

Estimate:

the room temperature.