SOLUTION: The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^0.05t where k is a constant and t is the time in years.

Question 319108: The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^0.05t where k is a constant and t is the time in years. If the current population is 36,000, in how many years is the population expected to be 90,000? (Round to the nearest year.)
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
P(t) = 1 + ke^(0.05t)
Let P(t) = 90,000 , 36,000 = 1 + k
and k = 35,999
90,000 = 1 + 35,999e^(0.05t)
Can you take it from here?

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