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?

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%