SOLUTION: The population of a particular city was 22 million in 1984; in 1994, it was 31 million. The exponential growth function A=22e^kt describes the population of this country t years af

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The population of a particular city was 22 million in 1984; in 1994, it was 31 million. The exponential growth function A=22e^kt describes the population of this country t years af      Log On


   

Question 1158515: The population of a particular city was 22 million in 1984; in 1994, it was 31 million. The exponential growth function A=22e^kt describes the population of this country t years after 1984. Use the fact that 10 years after 1984 the population increased by 9 million to find k to three decimal places.
Answer by Shin123(626) About Me  (Show Source):
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Assuming that the function describes the population in millions, we have 22e%5E%2810k%29=31. Dividing both sides by 22, we have e%5E%2810k%29=31%2F22. Taking the natural logarithm of both sides, we get ln%28e%5E%2810k%29%29=ln%2831%2F22%29. 10k=ln%2831%2F22%29 So k=ln%2831%2F22%29%2F10. Using a calculator to approximate, we have k=0.034.