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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%

Respuesta :

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

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

which can be written as

[tex] P=25,000(1+0.0095)^t [/tex]

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

So

The daily growth is given by

[tex] P=25,000(1+\frac{0.0095}{365})^{365t} [/tex]

And the approximate daily growth rate is

[tex] \frac{0.0095}{365} *100 [/tex]

= 0.003%

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