3­2 Exponential and Logistic Modeling
Exponential Population Model
If r > 0, exp. growth
P(t) = P 0(1 + r)t
If r < 0, exp. decay
Jan 24­11:39 AM
Find growth/decay rate
P(t) = 3.5(1.09) t
Find the exponential function.
Initial value = 5, increasing at a rate of 17% per year
Initial mass = .6, doubling every 3 days
Jan 24­11:47 AM
1
Radioactive decay
Half­life: time for half to be gone (or remain)
The half­life of a certain radioactive substance is 14 days. There are 6.6 g present initially.
a) Express the amount of substance remaining as a function of t.
b) When will there be less than 1 g remaining?
Jan 24­11:56 AM
Find the logisic function that satisfies the given conditions.
Initial value = 10, limit to growth = 40, passing through (1,20)
Jan 17­10:16 AM
2
The number of students infected with the flu at Trinity after
t days is modeled by the given function.
P(t) =
800
1 + 49e­.2t
a) What was the inital number of infected students?
b) When will the number of infected students be 200?
Jan 25­8:57 AM
pg.296 #4 ­ 32 (4th), 34, 40, 46
Jan 25­9:04 AM
3
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4
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5
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6