A certain country's factory sales of electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.0389t^3 + 0.495t^2 + 5.699t + 43.6, where output is measured in billion dollars and t is the number of years since 1990. (a) Calculate the average annual value of the country's factory sales of electronic goods to dealers from 1990 through 2001. (Round your answer to three decimal places: = billion dollars) (b) Calculate the average rate of change of the country's factory sales of electronic goods to dealers from 1990 through 2001. (Round your answer to three decimal places: billion dollars per year)
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Given function: \( s(t) = 0.0389t^3 + 0.495t^2 + 5.699t + 43.6 \) Average annual value = \( \frac{1}{11} \int_{0}^{11} s(t) dt \) Integrating the function: \( \frac{1}{11} \left[ 0.0389 \cdot \frac{t^4}{4} + 0.495 \cdot \frac{t^3}{3} + 5.699 \cdot \frac{t^2}{2} + Show more…
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The rate of change of annual U.S. factory sales (in billions of dollars per year) of a certain class of goods to dealers from 1990 through 2001 can be modeled as: s(t) = 0.121t^2 - 1.02t + 5.72 billion dollars per year where t is the number of years since 1990. Check: s(2) = 4.164 (c) If factory sales were $43.5 billion in 1990, what were they in 1999? (Round your answer to three decimal places.) $ billion
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Electronics Sales (1990s) Annual U.S. factory sales of consumer electronics goods to dealers from 1990 through 2001 can be modeled as $$ s(t)=0.0388 t^{3}-0.495 t^{2}+5.698 t+43.6 $$ where output is measured in billion dollars and $t$ is the number of years since $1990 .$ (Sources: Based on dara from Statistical Abstract, 2001 ; and Consumer Electronics Association) a. Numerically estimate to the nearest tenth the derivative of $s$ when $t=10$. b. Interpret the answer to part $a$.
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Electronics Sales (1990s) Annual U.S. factory sales of consumer electronics goods to dealers from 1990 through 2001 can be modeled as $$ s(t)=0.0388 t^{3}-0.495 t^{2}+5.698 t+43.6 $$ where output is measured in billion dollars and $t$ is the number of years since $1990 .$ (Sources: Based on data from Statistical Abstract, 2001 ; and Consumer Electronics Association a. Numerically estimate to the nearest tenth the derivative of $s$ when $t=10$ b. Interpret the answer to part $a$.
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