5.5 Exporential Growth and decay
day=ky, yco) = yo
f = ky
[ Gample of
differential
equation
а
* Grumple of an initial value
problem. Ia differential equation
an initial condition).
1
with
"The growth of y is proportional to the current value of
kt
y."
Mote: y(t)=Cc
is a solution of # = kg "/c
dyż kl eth
=
K(Cek+) -ky
But what is c?
ylos - Ce
*(0);
dy
Theorems: The Only solutions of the 4 ky
g(f) = ylode! often write
их
Yo =y(0)
2x. The US population was 282 million in 2000 and
328 million in 2014.
al Find a model (functional for the US population +
years 2000 assuming the growth of the population
P(+) = Pookk to it's current size.
t.
+ = years since 2000
P = milling of people in the us
P(0)=252 and P(19)=3285
я
P(+)=28+,
₤4
use this is nd Ic
fi
day=ky, yco) = yo
f = ky
[ Gample of
differential
equation
а
* Grumple of an initial value
problem. Ia differential equation
an initial condition).
1
with
"The growth of y is proportional to the current value of
kt
y."
Mote: y(t)=Cc
is a solution of # = kg "/c
dyż kl eth
=
K(Cek+) -ky
But what is c?
ylos - Ce
*(0);
dy
Theorems: The Only solutions of the 4 ky
g(f) = ylode! often write
их
Yo =y(0)
2x. The US population was 282 million in 2000 and
328 million in 2014.
al Find a model (functional for the US population +
years 2000 assuming the growth of the population
P(+) = Pookk to it's current size.
t.
+ = years since 2000
P = milling of people in the us
P(0)=252 and P(19)=3285
я
P(+)=28+,
₤4
use this is nd Ic
fi
