SOLUTION: use the formula P=Po^ekt. a bacterial culture has an initial population of 10,000. if its population declines to 7000 in 2 hours, a.) find the exponential model for this data b.)

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Question 281904: use the formula P=Po^ekt. a bacterial culture has an initial population of 10,000. if its population declines to 7000 in 2 hours,
a.) find the exponential model for this data
b.) what will the population be at the end of 4 hours
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
At time t=0, P=10000.
P=P0%2Ae%5E%280%29=P0=10000
P0=10000
At time t=2, P=7000.
P=10000%2Ae%282k%29=7000
e%282k%29=0.7
2k=-0.3567
k=-0.1783
.
.
.
P%28t%29=10000e%5E%28-0.1783t%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
use the formula P=Po^ekt. a bacterial culture has an initial population of 10,000. if its population declines to 7000 in 2 hours,
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initial population = Po = 10,000
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a.) find the exponential model for this data
Find k if t=2 hrs.
7000 = 10,000*e^(k(2))
e^(2k) = 0.7
Take the natural log and solve for "k":
2k = ln(0.7)
k = -0.1783
----------------------
Model: P(t) = 10,000*e^(-0.1783t)
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b.) what will the population be at the end of 4 hours
P(4) = 10,000*e^(-0.1783*4)
P(4) = 10,000*0.49
P(4) = 4900
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Cheers,
Stan H.