The annual consumption of beef per person was about 64.8 lb in 2000 and about 60.1 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 10 lb?

Question

Rios

Mathematics

29 November, 04:29

The annual consumption of beef per person was about 64.8 lb in 2000 and about 60.1 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 10 lb?

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Tori Meyer · Answer 1

a) B (t) = 64.8e^ (-0.01255t), k=-0.0125 b) 56.5 c) 2150

Step-by-step explanation:

a) B (t) = Ae^ (-kt)

at t=0, B (t) = 64.8

A=64.8

at t=6, B (t) = 60.1

60.1=64.8e^ (-6k)

k=0.0125

b) B (t) = 64.8e^ (-0.0125*11)

B (t) = 56.5

c) 10=64.8e^ (-0.0125t)

0.15432=e^ (-0.0125t)

-0.0125t=ln (0.15432)

-0.0125t=-1.869

t=149.5 or 150

Year = 2150