Because of an insufficient oxygen supply, the trout population in a lake is dyin
ID: 2855661 • Letter: B
Question
Because of an insufficient oxygen supply, the trout population in a lake is dying. The population's rate of change can be modeled by dp/dt= 115et/30 where t is the time in days. When t = 0, the population is 3450. (a) Find a model for the population. P(t) = (b) What is the population after 14 days? (Round your answer to the nearest integer.) fish (c) How long will it take for the entire trout population to die? (Assume the entire population has died off when the population is less then one. Round your answer to one decimal place.) days
Explanation / Answer
a)GIVEN dp/dt= 115et/30
getting equation in variable seperable form
dp= 115et/30 dt
integrate on both sides
dp= 115et/30 dt
P=[-115/(-1/30)]e-t/30 +c
P=3450e-t/30 +c
given When t = 0, the population is 3450
34050=3450e0+c
=>3450=3450+c
=>c=0
P=3450e-t/30
b)for the population after 14 days
P=3450e-14/30
P=2164 fish
c)Assume the entire population has died off when the population is less then one
1=3450e-t/30
e-t/30=1/3450
-t/30=ln(1/3450)
-t/30=-8.14613
t=244.4 days
it take 344.4 days for the entire trout population to die