The relative growth rate r of a function f measures the change in the function compared to its value at a particular point. It is computed as r(t)=
f′(t)
f(t). A logistic growth model for a certain population with a base population of 6 ​individuals, carrying capacity of 15 ​individuals, and a base growth rate of 0.025 is shown below. Complete parts​ (a) through​ (c).
P(t)=
90
6+9e−0.025t
Question content area bottom
Part 1
a. Is the relative growth in 1999 ​(t=​0) for the logistic model of the above population equal to r(0)=
P′(0)
P(0)=0.013 ​(rounding to three decimal​ places)? This would mean that the population was growing at 1.3​% per year.
Yes
Yes
No
No
Your answer is correct.
Part 2
b. Compute the relative growth rate of the population in 2005 and 2020. What appears to be happening to the relative growth rates as time​ increases?
​r(6​)=enter your response here
​r(21​)=enter your response here
​(Round to four decimal places as​ needed.)