$$h ( t ) = \frac { d ^ { 2 } f ( t ) } { d t ^ { 2 } }$$

question 17

Essay

$$\text { Let } \mathrm { f } ( \mathrm { t } ) = 2 \cos ( 5 \mathrm { t } ) \mathrm { u } ( \mathrm { t } ) \text {. Find the one-sided Laplace transform of } \mathrm { f } ( \mathrm { t } ) , g ( t ) = \frac { d f ( t ) } { d t } \text {, and }$$ $$h ( t ) = \frac { d ^ { 2 } f ( t ) } { d t ^ { 2 } }$$

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Definitions:

Annual Interest Rate

The percentage of a sum of money charged for its use per year.

Compounded Continuously

A way of calculating interest where the frequency of compounding is so high that it is effectively continuous, leading to exponential growth.

Exponential Equation

An equation in which a variable appears in the exponent, showing the rate of growth or decay.

Exponential Model

A mathematical representation of a situation where growth or decay rate is proportional to the current value, leading to rapid increases or decreases.