# The temperature T in ""^oC of a particular city during a 24 hour period can be modelled by T = 10 + 8 sin 12 pi t where t is the time in hours, with t = 0 corresponding to midday. Find the rate at which the temperature is changing at 4pm.?

May 23, 2018

${96}^{\circ} C / h o u r$

#### Explanation:

$T = 10 + 8 \sin 12 \pi t$

When it is $1200$ time, $t = 0$.

When it is $1600$ time, $t = 4$.

$\frac{\mathrm{dT}}{\mathrm{dt}} = 96 \cos 12 \pi t$

When $t = 4$,

$\frac{\mathrm{dT}}{\mathrm{dt}} = 96 \cos 48 \pi$
$\textcolor{w h i t e}{\frac{\mathrm{dT}}{\mathrm{dt}}} = 96$