OXYGEN CONTENT OF A POND The oxygen content t days after organic waste has been dumped into a pond is given by f ( t ) = 100 ( t 2 + 10 t + 100 t 2 + 20 t + 100 ) percent of its normal level. a. Show that f (0) = 100 and f (10) = 75. b. Use the Intermediate Value Theorem to conclude that the oxygen content of the pond must have been at a level of 80% at some time. c. At what time(s) is the oxygen content at the 80% level? Hint: Use the quadratic formula .
OXYGEN CONTENT OF A POND The oxygen content t days after organic waste has been dumped into a pond is given by f ( t ) = 100 ( t 2 + 10 t + 100 t 2 + 20 t + 100 ) percent of its normal level. a. Show that f (0) = 100 and f (10) = 75. b. Use the Intermediate Value Theorem to conclude that the oxygen content of the pond must have been at a level of 80% at some time. c. At what time(s) is the oxygen content at the 80% level? Hint: Use the quadratic formula .
Solution Summary: The author demonstrates the value of f(0)=100 and
OXYGEN CONTENT OF A POND The oxygen content t days after organic waste has been dumped into a pond is given by
f
(
t
)
=
100
(
t
2
+
10
t
+
100
t
2
+
20
t
+
100
)
percent of its normal level.
a. Show that f(0) = 100 and f(10) = 75.
b. Use the Intermediate Value Theorem to conclude that the oxygen content of the pond must have been at a level of 80% at some time.
c. At what time(s) is the oxygen content at the 80% level?
Hint: Use the quadratic formula.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
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