Question

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

Answer 1

Daily growth rate: 0.003%

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

Answer 2

Answer:

The approximate daily growth rate is 0.0026%

The function can be rewritten as P = 25,000*[1.0095^(1/365)]^t, where now t is in days

Step-by-step explanation:

Given the formula:

P = 25,000*(1.0095)^t

25,000 indicates the initial population, t is the time elapsed in years, and P is the population after t years. After 1 year the population will be:  

P = 25,000*(1.0095)

which is equivalent to:

P = 25,000*100.95%

that represents an increment of 0.95 % in a year. Given that the year has 365 days, then this represent a daily growth of 0.95/365 = 0.0026%

Dividing t by 365 in the original expression, so that, time is expressed in days, we get:

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

Which can be rewritten as:

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

P = 25,000*(1.000026)^t

That represents a daily growth rate of 0.0026% and now t is in days