MATH SOLVE

2 months ago

Q:
# A city's population is represented by the function P=25,000 (1.0095) t , where t is time in years. How could the function be rewritten to identify the daily growth rate of the population? What is the approximate daily growth rate?

Accepted Solution

A:

We are given the following function:
P = 25,000 (1.0095)^t
However the given function is in the basis of 1 year. We
know that in 1 year there are 365 days, therefore we must place a (1/365)
exponent to the overall rate (1.0095) and divide the time (t) by 365 to get a
function on the basis of per day. Hence:
P = 25,000 [1.0095^(1/365)]^(t / 365)
The rate is equal to the term:
rate = 1.0095^(1/365)
– 1
Calculating for the rate:
rate = 1.000025905 – 1
rate = 0.000025905 or 0.003%
Summary of answers:
>P = 25,000 [1.0095^(1/365)]^(t / 365)
>0.003%