2.3 Rates of Change Group Review
AP Calculus
1. The accompanying figure shows the velocity v = f (t) of a particle moving on a coordinate line.
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2. A rock thrown vertically upward from the surface of the moon at a velocity of 42 mlsec reaches a height of
s = 42t - 0.8t2 meters in t seconds.
a. Find the rock's velocity and acceleration attime t. 'V{-l::}:;:::s' (·f):::b. How long does it take the rock to reach its highest point?
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e. How long is the rock aloft?
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3. Find the general formula for F"(x) if F(x)
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4. Find a function y = or + bx + c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with a
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6. According to Newton's Law of Cooling, the rate of change of an object's temperature is proportional to the difference
between the temperature of the object and that of the surrounding medium. The accompanying figure shows the graph
of the temperature T (in degrees Fahrenheit) versus time t (in minutes) for a cup of coffee, initially with a temperature
of 200 F , that is allowed to cool in a room with a constant temperature of 75 F .
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A. Estimate T and dT/dt when t = 10 min.
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B. Newton's Law of Cooling can be expressed as -=k(T -Yo) where kis the constant of proportionality and
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7. Suppose that a product currently sells for $25, with the price increasing at the rate of $2 per year. At this current price,
consumers will buy 150 thousand items, but the number sold is decreasing at the rate of 8 thousand per year. Revenue
= quantity x price, since these quantities are changing in time, we write R(t) = Q(t)P(t),
where R(t) is revenue, Q(t)
is quantity sold and P(t) is the price, all at.time
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At what rate is the total revenue increasing or decreasing?