SOLUTION: Hello, The population P of mice after t years is modeled by the function P(t)= 1200/1 +99e^-0.4t a-what was the initial population of mice b-when will there be 1000 mice

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, The population P of mice after t years is modeled by the function P(t)= 1200/1 +99e^-0.4t a-what was the initial population of mice b-when will there be 1000 mice       Log On


   



Question 684278: Hello,
The population P of mice after t years is modeled by the function P(t)= 1200/1 +99e^-0.4t
a-what was the initial population of mice
b-when will there be 1000 mice
c-what is the carring capacity for the mice population

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The population P of mice after t years is modeled by the function P%28t%29=+1200%2F%281+%2B99e%5E%28-0.4t%29%29

a) To find the initial population, plug in 0 for t
P%280%29+=+1200+%2F+%281+%2B+99e%5E%28-0.4%2A0%29%29
P%280%29+=+1200+%2F+%281+%2B+99e%5E%280%29%29
P%280%29=+1200+%2F+%281+%2B+99%29
P%280%29=+1200%2F100
P%280%29=+12
b) To find when there will be 1000 mice, P(t) will equal 1000
1000+=+1200+%2F+%281%2B+99e+%5E%28-0.4t%29%29
1%2B+99e+%5E%28-0.4t%29+=+1200%2F1000+=+1.2
99e+%5E%28-0.4t%29+=+1.2+-+1+=+.2
e+%5E%28-0.4t%29+=+.2%2F99
-.4t+=+ln%28.2%2F99%29
t+=+ln%28.2%2F99%29%2F-.4
t+=+15.5113 years

c) The maximum value of mice will be 1200. To do this, simply graph it on a graphing calculator and find the maximum. It approaches 1200.