SOLUTION: Following the function P(t)=1+ke^0.08t where k is a constant and t is the time in years. If the current population is 37,000 in how many years is the population expected to be 92,

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Question 1010020: Following the function P(t)=1+ke^0.08t where k is a constant and t is the time in years. If the current population is 37,000 in how many years is the population expected to be 92,500?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

P%28t%29=1%2Bke%5E%280.08t%29+where+%7B%7B%7Bk is a constant and t is the time in years.
k=37000
P%28t%29=+92500
find: t
92500=1%2B37000e%5E%280.08t%29

92500-1=37000e%5E%280.08t%29

92499=37000e%5E%280.08t%29

92499%2F37000=e%5E%280.08t%29

2.499972972972973=e%5E%280.08t%29........take a natural log of both sides

ln%282.499972972972973%29=ln%28e%5E%280.08t%29%29

ln%282.499972972972973%29=%280.08t%29ln%28e%29-----ln%28e%29=1

ln%282.499972972972973%29=0.08t%0D%0A%0D%0A%0D%0A%7B%7B%7Bt=ln%282.499972972972973%29%2F0.08

t=0.9162799210049070%2F0.08

t=11.4534990125613375

t=11.5->t=111%2F2 years