SOLUTION: the population P of a city is given by P=2500eto the exponent of kt, where is the number of years, with t=0 corresponding to the year 1990. In 1945, the population was 1350. Find t

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NOTE: For more examples like this one "In Living Color" see my Lesson Plan "Population Growth" in the topic "Logarithm" in algebra.com.



P= 1350 in 1945 when t= -45 (45 years before 1990)


Divide both sides by 2500:


Take the ln of both sides:


Divide both sides by -45:

k = .0136930253 approximately.

If you have a graphing calculator, store that value, and then use the calculator to evaluate the following, when t= 20 (years from 1990 to 2010) and k is the value from the calculator above:

or

NOTE: This problem can also be solved by letting the initial population be 1350 in year 1945, letting P= 2500 when t=45 in 1990. The value of k is EXACTLY the same! Then, to find the population in the year 2010, using the initial population of 2500, use the value of t = 20 years from 1990 to 2010. The result is EXACTLY the same!! Try it!!

R^2 at SCC

P.S. Do I get THREE points for solving this same problem THREE times???