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Q16 E

Expert-verifiedFound in: Page 5

Book edition
9th

Author(s)
R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages
616 pages

ISBN
9780321977069

**In Problems 13-16, write a differential equation that fits the physical description. The rate of change of the mass A of salt at time t is proportional to the square of the mass of salt present at time t.**

The differential equation suitable for the given condition is $\frac{\mathrm{dA}}{\mathrm{dt}}={\mathrm{A}}^{2}$, where A is the mass of salt at a time t.

By analyzing the given statement,

$\frac{\mathrm{dA}}{\mathrm{dt}}\propto {\mathrm{A}}^{2}$, where A is the mass of salt at a time t.

$\frac{\mathrm{dA}}{\mathrm{dt}}={\mathrm{kA}}^{2}$, where k is the constant of proportionality.

**Hence, $\frac{\mathbf{dA}}{\mathbf{dt}}{\mathbf{=}}{{\mathbf{kA}}}^{{\mathbf{2}}}$ is the required differential equation.**

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