2011 AP Calc AB FRQ #5 part c
Warm-up: At the beginning of 2010, a landfill contained 1400 tons of
solid waste. The increasing function W models the total amount of solid
waste stored at the landfill. Planners estimate that W will satisfy
the differential equation
for the next 20 years.
W is measured in tons, and t is measured in years from the start of 2010.
c. Find the particular solution W = W(t) to the differential equation
with initial condition W(0) = 1400.
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6.3 Differential Equations
Example 1:
Solve
for a general solution.
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Example 2:
Solve this differential equation for a specific
solution through the origin.
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Example 3:
Solve for a general solution
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Example 4: Solve the following differential equation with the initial
condition of (0,1).
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Example 5: Solve the following differential equation with the initial
condition of (0,1).
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Exponential Growth and Decay
The rate the amount
increases or decreases
is
proportional to
the amount present
y = that is solved for represents the quantity (population, radioactive
element, money) that increases or decreases at a rate proportional
to the amount present
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Solve the differential equation on the previous page:
If given an initial condition, y = y0 when t = 0, you solve the
initial value problem
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Note:
is the proportionality constant.
Law of Exponential Change:
Compounded Interest:
Continuously Compounded
Interest:
Radioactivity:
Half-Life:
Newton's Law of Cooling:
Resistance Proportional to
Velocity:
Coasting Distance:
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Example 6: The rate of change of y is proportional to y.
When t=0, y=2. When t=2, y=4. What is the value of y
when t=3?
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Example 7: Find the solution to the differential equation
that satisfies the given conditions:
,
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Example 8: Suppose an experimental population of fruit
flies increases according to the law of exponential growth.
There were 100 flies after the second day of the experiment
and 300 flies after the fourth day. Approximately, how many
flies were in the original population?
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