AP CALCULUS BC - AP REVIEW 3
Work these on notebook paper.
Use your calculator only on problems 25 and 29.
25. (Calc)
The tide removes sand from Sandy Point Beach at a rate modeled by the function
R
, given by
4
2
5sin
.
25
t
R t
A pumping station adds sand to the beach at a rate modeled by the function
S
,
given by
15
.
1
3
t
S t
t
Both
R t
and
S t
have units of cubic yards per hour and
t
is measured in
hours for
0
6.
t
At time
t
= 0, the beach contains 2500 cubic yards of sand.
(a) How much sand will the tide remove from the beach during this 6-hour period?
Indicate units of
measure.
(b) Write an expression for
,
Y t
the total number of cubic yards of sand on the beach at time
t
.
(c) Find the rate at which the total amount of sand on the beach is changing at time
t
= 4.
(d) For
0
6,
t
at what time
t
is the amount of sand on the beach a minimum?
What is the minimum
value?
Justify your answer.
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