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The annual consumption of beef per person was about 64.9 lb in 2000 and about 60.7 lb in 2007. 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 2013. ​c) In what year​ (theoretically) will the consumption of beef be 30 ​lb?

Respuesta :

Answer:

Step-by-step explanation:

given that the annual consumption of beef per person was about 64.9 lb in 2000 and about 60.7 lb in 2007.

Assume​ B(t), the annual beef consumption t years after​ 2000, is decreasing according to the exponential decay model

i.e. [tex]B(t) = B_0 e^{-kt}[/tex], where t is the number of years from 2000

B0 = quantity in 2000 = 64.9

So the equation is

[tex]B(t) = 64.9 e^{-kt}[/tex]

When t =7, B(7) = 60.7

Substitute to solve for k

[tex]60.7 = 64.9 e^{-7k}\\\\e^{-7k}=0.9353\\k =0.009557[/tex]

So equation woul dbe

[tex]B(t) = 64.9e^{-0.0096t}[/tex]

c) B(t) = 30 gives

[tex]30= 64.9e^{-0.0096t}\\t = 80.38[/tex]

i.e. in the year 2080

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