3 lim 8 x e x + 1 lim e t t - - cos cos lim mx nx x

AP Calculus Review
9.2 L’Hopital
7.4 Exponential Growth/Decay
3x  e x
x 
8x
Name: ____________________
2.
lim
et  1  t
t2
3.
( x 3  8)
lim
x  2 ( x  2)( x  2)
4.
lim
cos mx  cos nx
x2
5.
lim
ln 3 x
x  x 2
6.
lim(ln x)1/ x
1.
lim
t 0
x 0
x 
7.
9.
cos x
x 0
x
lim xe x
8.
lim
1  e2 x
lim
x 0 sec x
x 
10.
lim
ln x
x 
x
1
2
11.
Titanium-38 has a ½ life of 450 yrs. How much Titanium-38 will be left in 30 yrs if if
decays at a rate proportional to the quantity present and it begins at 17 lbs.
12.
An investment of $4000 grows at a rate of
Its value after 10 years is approximately
A)
$4902
B)
$8902
C)
dP
 320e 0.08t dollars per year after t years.
dt
$7122
D)
$12,902
E)
none
13.
At any time t> 0, in days, the rate of growth of a bacteria population is given by
dy
 ky ,
dx
where k is a constant, and y is the number of bacteria present. The initial population is
1,000 and the population triples after five days.
(a)
Write an expression for y at any time t > 0
(b)
By what factor will the population have increased in the first 10 days?
(c)
At what time t, in days, will the population have increased by a factor of 6?
14.
The decay equation for radon-222 gas is known to be y  y0 e 0.18t , with t in days. About
how long will it take the radon in a sealed sample of air to lose 10% of its original value?
15.
The concentration of bacteria in a culture increases at a rate proportional to the number
present. In other words, the rate of growth of a bacteria population is given by
dy
 ky ,
dt
where y is the number of bacteria present and k is a constant of proportionality. If the
constant of proportionality is 11% per hour, in how many hours will the concentration
triple?
16.
A cup of coffee placed on a table cools at a rate of
dH
dt
 0.05(H  70) degrees per
minute, where H represents the temperature of the coffee and t is time in minutes. If
the coffee was at 120ºF initially, what will its temperature be 10 minutes later?
A)
73ºF
B)
95ºF
C)
100ºF
D)
118ºF
E)
143ºF

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