Question

A city's population is represented by the function P=25,000(1.0095)t P=25,000(1.0095)t , where t is time in years.

How could the function be rewritten to help identify the daily growth rate of the population? What is the approximate daily growth rate?


Function

P= 25,000 (1.00095 ^1/365t) ^365t



Functions:

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

P = 25,000 (1 + 0.0095) ^t/365

P = 25,000 (1 + 0.0095 ^1/365) ^365t


Daily Growth Rates:

0.003%

0.95%

0.0012%

Answer 1

To convert the function representing the yearly growth of population , to the function representing the daily growth of population we divide the rate of increase by 365 , as there are 365 days in a year.

Now the given function is

`P=25,000(1.0095)^t`

which can be written as

`P=25,000(1+0.0095)^t`

It means the yearly rate of increase is 0.0095, we divide it by 365

So

The daily growth is given by

`P=25,000(1+(0.0095)/(365))^(365t)`

And the approximate daily growth rate is

`(0.0095)/(365) *100`

= 0.003%