For Question $1$ refer to the following problem statement:

This example deals with Newton's law of cooling, which states that the temperature, $T,$ of a relatively small object placed in the medium with temperature Tomer changes at the rate proportional to the difference between the temperature of the object and ambient temperature. It can be expressed as:

$\frac{dT}{dt}=-k(T-T_{-})$

where $k$ is a positive constant measured in Kelvins$/$second $(\frac{K}{s}),$ and $r$ is the time in seconds. Assume that the initial value of the object temperature is $T.$ Determine the temperature as a function of time.

Q$\mathrm{.}1$: What is the temperature $(T)$ of the body at $t=5sec?$ Assume $k=0\mathrm{.}1,T=100F,$ and $T=40F.$

For Question $2$ refer to the following problem statement:

This example deals example deals with phenomenon of radioactive decry. Most radioactive materials disintegrate at a rate propertional to the amount present at a given time $t.$ Let $Q(t)$ represent the amount at any time $f$ and $Q_0$ represent the initial quantity. The rate of change of material is then governed by the following differential equation

$\frac{dQ}{dr}=-rQ$

where $r$ is a positive rate of decay. Determine a solution for the amount of material as a function of time.

Q$\mathrm{.}2$: How much of radioactive material is left affer $1000$ years? Assume $r=1\mathrm{.}21{10}^{-1}1$ year, and $Q=1kg.$