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?

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. , where t is the number of years from 2000

B0 = quantity in 2000 = 64.9

So the equation is

When t =7, B(7) = 60.7

Substitute to solve for k

So equation woul dbe

c) B(t) = 30 gives

i.e. in the year 2080

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus