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Table 10.18 gives data on strawberry production from 2008 through 2012, where t

ID: 3148493 • Letter: T

Question

Table 10.18 gives data on strawberry production from 2008 through 2012, where t is in years since 2008. Let f_{CA}(t) , f_{FL}(t), and f_{US}(t)be the harvested area in year t for strawberries grown in California, Florida, and the US overall, respectively.

Likewise, letg_{CA}(t) ,g_{FL}(t) , andg_{US}(t) give the yield in thousands of pounds per acre for these three regions. Let h_{CA}(t)= f_{CA}(t)g_{CA}(t) Create a table of values forh_{CA}(t) for0t4 . Describe in words what h_{CA}(t)tells you about strawberry production.

t CA FL US total CA FL US total 0 37,600 7100 54,700 60.5 26.0 45.6 1 39,800 8800 58,080 62.0 27.0 48.2 2 38,600 8800 56,900 67.0 22.0 50.1 3 38,000 9900 57,420 68.0 25.0 50.8 4 38,500 8700 56,140 72.0 21.0 53.7

Explanation / Answer

In question it is given that,
f_{CA}(t) = harvested area for strawberries grown in California,
f_{FL}(t) = harvested area for strawberries grown in Florida and
f_{US}(t) = harvested area for strawberries grown in US

Also,

g_{CA}(t) = yield in thousands of pounds per acre for California
g_{FL}(t) = yield in thousands of pounds per acre for Florida
g_{US}(t) = yield in thousands of pounds per acre for UA

and the first column of the given table defines year, where
0 is 2008
1 is 2009
2 is 2010
3 is 2011 and
4 is 2012.

Now, we need to make a table for:
h_{CA}(t)= f_{CA}(t)g_{CA}(t) from 2008 through 2012.

For 2008,
f_{CA}(t) = 37,600 (considering it to be in acres) and
g_{CA}(t) = 60.5 thousands of pounds/acre = 60500 pounds/acre
Therefore, h_{CA}(t) = 37600*60500 = 2274800000 pounds = 2274800 thousands of pounds

Similarly, h_{CA}(t) for,
2009 will be, 2467600 thousands of pounds
2010 will be, 2586200 thousands of pounds
2011 will be, 2584000 thousands of pounds
2012 will be, 2772000 thousands of pounds.

Table for h_{CA}(t):

(t)


Now, h_{CA}(t) = f_{CA}(t)g_{CA}(t) i.e.
h_{CA}(t) = harvested area for strawberries grown in California * yield in thousands of pounds per acre for California

which means h_{CA}(t) will give the total yield for California in thousands of pounds for the entire harvested area from 2008 through 2012 i.e. total yield for strawberries grown in California in the entire harvested area available from 2008 through 2012.

Year

(t)

f_{CA}(t) (in acres) g_{CA}(t) (in thousands of pounds) h_{CA}(t) (in thousands of pounds) 0(2008) 37600 60.5 2274800 1(2009) 39800 62 2467600 2(2010) 38600 67 2586200 3(2011) 38000 68 2584000 4(2012) 38500 72 2772000

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