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
