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The Strength of a Tree Branch Is Approximately Proportional to Its

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Essay

The strength of a tree branch is approximately proportional to its cross-sectional area while its weight is proportional to its volume.If you "scale up" a tree branch by a factor of two (double all of its linear dimensions) by what factor is its strength increased? By what factor is its weight increased?


Definitions:

Present Value

The current value of a future sum of money or stream of cash flows given a specified rate of return.

Compounded Quarterly

The method of calculating interest where the interest is added to the principal sum four times a year.

Compounded Annually

A method of calculating interest where the interest earned over a year is added to the principal, and the sum becomes the principal for the next year.

Future Value

The value of an investment or loan at a specific date in the future, calculated using the current value and the expected rate of growth or interest.

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