Real-Life Math -- Solution
Last year, the National Corn Grower's Society asked you, a
professional plant physiologist, to research the effectiveness of a new nitrogen
fertilizer they developed. You planted 5 acres of corn and used different
amounts of fertilizer on each acre. At the end of the growing season, you
tallied (in bushels) the yield that each acre produced. Now you have to do
the math to determine whether this fertilizer is cost-effective for the society's
members.
"A large part of what we do is math-driven," says plant science
professor Norm Hopper. "When we analyze data or try to match the application
of fertilizers or crop protection chemicals to the response of the plants,
we often use statistics and numbers."
While the National Corn Grower's
question may seem complicated, the math is actually quite easy. For the first
acre, 0 pounds of fertilizer were used, and 100 bushels of corn were produced.
If the fertilizer costs $1 a pound, and bushels sell for $2, then the math
to determine the profit a farmer would have made from the first acre is:
0
pounds of fertilizer x $1 per pound = $0 spent
100 bushels x $2 per bushel
= $200 earned
$200 earned - $0 spent = $200 profit
For
the second acre the math is:
40 pounds x $1 = $40 spent
120
bushels x $2 = $240 earned
$240 - $40 = $200 profit
For
the third acre the math is:
80 pounds x $1 = $80 spent
145
bushels x $2 = $290 earned
$290 - $80 = $210 profit
For
the fourth acre the math is:
120 pounds x $1 = $120 spent
170
bushels x $2 = $340 earned
$340 - $120 = $220 profit
For
the fifth acre the math is:
160 pounds x $1 = $160 spent
170
bushels x $2 = $340 earned
$340 - $160 = $180 profit
Based
on the results of your experiment and the math calculations you performed,
you informed the National Corn Grower's Society that buying 120 pounds
of the new nitrogen fertilizer for each acre of corn planted will produce
the greatest profit ($220 per acre) for those who use it.
"The example
we've created is typical in that you'll see a nitrogen fertilizer
increase yields, but only until a point where the plant's nitrogen need
is fulfilled, and then other limiting factors prevent the production of greater
yields even after the nitrogen fertilizer amounts are increased,"
says Hopper.