SOLUTION: Could someone please help explain how to solve for the years: The population of a small town is modeled by the equation P = 1650e^0.5t where t is measured in years. In appro

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Question 1129295: Could someone please help explain how to solve for the years:

The population of a small town is modeled by the equation
P = 1650e^0.5t where t is measured in years. In approximately how many years will the town's population reach 20,000? (Round your answer to two decimal places.)

Found 2 solutions by stanbon, IsleofSkye:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The population of a small town is modeled by the equation
P = 1650e^0.5t where t is measured in years. In approximately how many years will the town's population reach 20,000? (Round your answer to two decimal places.)
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Solve for "t"::
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20,000 = 1650*e^(0.5t)
e^(0.5t) = 12.12
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Since the variable is in the exponent, take the ln of both sides to get:
0.5t = ln(12.12) = 2.495
t = 4.99 years
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Cheers,
Stan H.
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Answer by IsleofSkye(1) About Me  (Show Source):
You can put this solution on YOUR website!
Thank you so so much for explaining how to correctly solve this, and future problems alike. It is greatly appreciated!