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