Page I I t: 201 J by Janice L. Epstein
3.3 RatCllofChonge in the ScIences
Rates of Change in the Sciences (Section 3.3)
The derivative as the instantaneous rate of change is important in
many applications.
EXAMPLE 1
The population of a bacterial colony after t hours is given by
n = 3t 2 2t + 500
Find and interpret n'(l) and n '(2)./
')\1
(t; -=- lo~-~
Y\"'(lJ=V\ \
bttL,
~
~(,)-~~Lf ~/~
('1.)--- (0(2-)-:1- -;::::.
'0
\t
"
EXAMPLE 2
The cost in dollars to produce x items is given by
. C(x) 100 + lOFx + 25x
Fmd the marginal cost C '() C
produce an additional item:; th omPdare C:'(x) to the actual cost to
items.
.-l
e pro uctlOn levels of 1 and 25
t I ('X ) =- b/~ -\-;.l...S ~) ~ \ 10 tf b, = $<A;{hY\ ~\l\)~ti30 j,km C (WJ-::' ~ 'IS) C:{2lp~'tD\ ~-=-~I tte'rr\
t( \J-::: \35 ) C,,(
C(w ):;:.
~lli M~YV\