Chapter : Differential Egas C DES )

Aws 10.1 due 4124

10.2 due 4124

Read 10.4 and 10.5

Marinette ( e. g."

wicked Tuna" )

PHI - fish populationC in 109 ) at time tcyeans )

-

no fishing DP r P ⇒ f PA ) -- Poe

't

allowed"

It Trothexponentially

\w r > 0

time nate -

of change

fishing

¥f=rPw- Nw N - # of fish

allowed"

groth fishing caught each year

Exe : {d Pldt

= IP - to

P ( o ) = 100 ( Plo ) = 20,

Pco) = so )

anti Iff -

- IP - to ⇒

lpftl-5otcets.TT#oyseparationof variables

C ? 100 = Plo) = 50 t C

e¥°=5OtC⇒c=5o_120-- P "

'IIe" "

pAi=5ot50eftp.?Ioc.e#so+cC--0

Piano

%¥Id¥hEP - " Ho

PHI -_ 50+50t . =¥ - 100-10=1030

equilibrium50mg

"

fso→oe±tao¥¥¥!¥¥o'

IsooEt}÷¥oE¥" "

--

50I

Equilibrium Sdn

Ex I.

In the graphs is shown the

temperature It (E) of 4 eggs

as a function of time tannate )

I

II

I

The Logistic Model-

function )

121 : L, GK > O PH ) = ¥e-kt

PfL - carrying capacity L -

.. . .

. . .. . . . . . . . . . . . . . .

. . . . .

1¥k - air:¥17711 42 )o.ci#i4a

)a

( -value to satisfy Rohlf po -

99 a-t

K

Point of Diminishing

Logistic DE K,

L > O 2 equilibrium sons

-

:

{¥tD⇒pea = I

salt -t

.'' Ito ¥# t

4¥,

" 4k¥ ) Iit :"Do

= K . # . I,

L 70