For this problem A is the variable for the amount of...

For this problem A is the variable for the amount of radioactive material, k is the growth constant (and assumed to be positive). The amount of radioactive material decreases at a rate proportional to the amount present. Write a differential equation to model the situation: Differential equation: -kA = 0 Find a formula for the half-life of the material: (ln2)/k Note: You can earn partial credit on this problem.

Radioactive Decay The amount of a radioactive substance decreases exponentially, with a decay constant of 3$\%$ per month. (a) Write a differential equation to express the rate of change. (b) Find a general solution to the differential equation from part (a). (c) If there are 75 $\mathrm{g}$ at the start of the decay process, find a particular solution for the differential equation from part (a). (d) Find the amount left after 10 months. Newton's Law of Cooling Newton's law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if $T$ is the temperature of the object after $t$ hours and $T_{M}$ is the (constant) temperature of the surrounding medium, then $$\frac{d T}{d t}=-k\left(T-T_{M}\right) $$ where $k$ is a constant. Use this equation in Exercises $61-64$

Differential Equations

Solutions of Elementary and Separable Differential Equations

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