©Zarestky
Math 151 Quiz 8 Version B
4/5/2010
NAME:__KEY_____________________________________
Section (circle one):
1.
507
508
509
510
511
512
A bacteria population starts with 100 rabbits and after 3 years, there are 700 rabbits. Assume the rabbit
population grows at a rate proportional to its size, without restriction.
A. (1 pt) What differential equation describes the growth of the population?
dy
= ky
dt
(OK to leave general k.)
B. (3 pts) Find a function to model the size of the population over time.
y (t ) = Ae kt
Initial value A = 100. Use the point (3, 700) to solve for k.
700 = 100e3k
1
e3k =
7
! 1$
3k = ln ### &&& = 'ln 7
" 7 &%
k=
2.
"$ !ln7 %'
't
$$
$# 3 ''&
The function is y (t ) = 100e
'ln 7
3
(3 pts)
" 1 % 2!
A. cos!1 $$! ''' =
$# 2 '&
3
(
)
B. cos tan!1 ( x ) =
3.
.
(3 pts) Evaluate lim
x!"
(1 pt)
1
x +1
2
(2 pts)
1
e #1
.
2x
x
The limit corresponds to the indeterminate form
e x #1
ex
= lim = "
x!" 2x
x!" 2
lim
x
x 2 +1
(2 pts)
!
. Use L’Hopital’s rule. (1 pt for verifying.)
!