Shrimp and Lobster

Question

The number of pounds (in millions) of shrimp (S) and lobster (L) consumed in the US from 1980 to 1990 can be modeled by S=42.8t+425 and L=-1.5t^2+20.7t+194.5 where t=0 for 1980. Find the model that represents the total amount (T) of shrimp and lobster consumed from 1980 to 1990. Estimate the amount (T) consumed in 1991.

Answer 1

Saif, this is easier than it seems, I promise!

 

First, we have to add our two polynomials by combining like terms.  We know that x + x = 2x, but x² + x² = 2x², also.  Anytime the degree or the variable changes, it becomes a different term.  x + y  cannot combine because they are two different terms. Neither can x + x².

 

So, if we put things in order by like terms, from both polynomials, we have 1.5t² + 20.7t + 42.8t + 194.5 + 425

 

Combining our like terms, we get 1.5t² + 63.5t + 619.5

 

Now, in order to estimate T for 1991, since 1980 was t = 0, then 1991 must be t = 11, right? 1981 is t = 1, 1982 is t = 2, etc.

 

So, we plug 11 in for every t.

 

1.5(11²) + 63.5(11) + 619.5 = 1499.5 pounds of shrimp and lobster.

 

Hope this helps!