Page 50 - How To Solve Word Problems In Calculus
P. 50
4
ρ(x) = m (x) = 4x −1/2 = √
x
ρ(4) = 2 slugs/ft
The movement of electrons through a wire produces an elec-
tric current. If Q is the charge flowing through the wire mea-
sured in coulombs, then the current I, measured in amperes,
is the rate of change of Q with respect to time in seconds.
EXAMPLE 10
The charge in coulombs that passes through a wire after t
seconds is given by the function
2
3
Q(t) = t − 2t + 5t + 2
(a) Determine the average current during the first two
seconds.
(b) Determine the current at the end of two seconds.
Solution
Q Q(2) − Q(0) 12 − 2
(a) I av = = = = 5 amperes
t 2 − 0 2
2
(b) I(t) = Q (t) = 3t − 4t + 5
2
I(2) = 3(2) − 4(2) + 5 = 9 amperes
EXAMPLE 11
The number of bacteria in a Petri dish after t hours is
3
2
n(t) = 2t + 5t + t + 2. How fast is the population growing
after 3 hours?
Solution
dn
2
= 6t + 10t + 1
dt
When t = 3, dn/dt = 85. The bacteria are growing at the rate
of 85 per hour.
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