Math Problem Statement
The annual consumption of beef per person was about 65.8 lb in 2000 and about 60.5 lb in 2006. Assume B(t), the annual beef consumption t years after 2000, is decreasing according to the exponential decay model. a) Find the value of k, and write the equation. b) Estimate the consumption of beef in 2011. c) In what year (theoretically) will the consumption of beef be 20 lb? Question content area bottom Part 1 a) Select the correct answer below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) A.Upper B left parenthesis t right parenthesis equals StartFraction 60.5 Over e Superscript negative left parenthesis nothing right parenthesis t EndFraction Upper B left parenthesis t right parenthesis equals StartFraction 60.5 Over e Superscript negative left parenthesis nothing right parenthesis t EndFraction B.Upper B left parenthesis t right parenthesis equals 65.8 e Superscript negative left parenthesis nothing right parenthesis t Upper B left parenthesis t right parenthesis equals 65.8 e Superscript negative left parenthesis nothing right parenthesis t C.Upper B left parenthesis t right parenthesis equals 60.5 e Superscript negative left parenthesis nothing right parenthesis t Upper B left parenthesis t right parenthesis equals 60.5 e Superscript negative left parenthesis nothing right parenthesis t D.Upper B left parenthesis t right parenthesis equals StartFraction 65.8 Over 60.5 e Superscript negative left parenthesis nothing right parenthesis t EndFraction Upper B left parenthesis t right parenthesis equals StartFraction 65.8 Over 60.5 e Superscript negative left parenthesis nothing right parenthesis t EndFraction
Solution
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Math Problem Analysis
Mathematical Concepts
Exponential Decay
Natural Logarithm
Formulas
Exponential decay formula: B(t) = B_0 * e^(-kt)
ln(B(t)/B_0) = -kt
Theorems
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Suitable Grade Level
Grades 9-12
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