The Function Graphed Is of the Form Y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$

question 260

Multiple Choice

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 8 \cos 20 \pi \mathrm { t }$ inches after $\mathrm { t }$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

• A) The maximum height of 8 inches is first reached after \(0.05\) seconds.
• B) The maximum height of 16 inches is first reached after 5 seconds.
• C) The maximum height of 8 inches is first reached after 10 seconds.
• D) The maximum height of 16 inches is first reached after 10 seconds.

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Definitions:

Business Cycle

The fluctuations in economic activity that an economy experiences over a period of time, characterized by periods of expansion (growth) and contraction (recession).

Recessions

Intervals of provisional economic contraction, during which commerce and industry slow down, often indicated by a dip in GDP across two sequential quarters.

Real GDP

The measure of a country's economic output adjusted for price changes (inflation or deflation), reflecting the true value of goods and services produced.

Recessions

Episodes of brief economic downturn where business and manufacturing activities decline, usually signaled by a decrease in the GDP for two back-to-back quarters.