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.

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

$P=25,000(1+\frac{0.0095}{365})^{365t}$

And the approximate daily growth rate is

$\frac{0.0095}{365} *100$

= 0.003%