A city's population is represented by the function P=25,000 (1.0095) t , where t is time in years. How could the function be rewritten to identify the daily growth rate of the population? What is the approximate daily growth rate?

Respuesta :

We are given the following function:

P = 25,000 (1.0095)^t

 

However the given function is in the basis of 1 year. We know that in 1 year there are 365 days, therefore we must place a (1/365) exponent to the overall rate (1.0095) and divide the time (t) by 365 to get a function on the basis of per day. Hence:

P = 25,000 [1.0095^(1/365)]^(t / 365)

 

The rate is equal to the term:

 rate = 1.0095^(1/365) – 1

Calculating for the rate:

rate = 1.000025905 – 1

rate = 0.000025905 or 0.003%

 

Summary of answers:

>P = 25,000 [1.0095^(1/365)]^(t / 365)

>0.003%

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