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) = TAT A logistic growth model for a certain population with a base population of 5 individuals, carrying capacity of 12individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c).60P(t) =5 +7e -0.025tP'(0)a. Is the relative growth in 1999 (t= 0) for the logistic model of the above population equal to r(0) == 0.015 (rounding to three decimal places)? This would mean that the population was growing at 1.5% per year.P(0)YesNob. Compute the relative growth rate of the population in 2005 and 2030. What appears to be happening to the relative growth rates as time increases?r(6) =r(31) =|(Round to four decimal places as needed.)What appears to be happening to the relative growth rates as time increases?O A. As time increases, the rate of population growth decreases.O B. As time increases, the rate of population growth increases.OC. As time increases, the rate of population growth nears the carrying capacity.O D. As time increases, the rate of population growth nears the initial population. P'(t)c. Evaluate lim r(t) = limP(t)where P(t) is the logistic growth function from above. What does your answer say about populations that follow a logistic growth pattern?t00t00lim r(t) =t00(Simplify your answer.)Choose the correct answer below.O A. As the population gets close to carrying capacity, the rate of population growth increases.O B. As the population gets close to carrying capacity, the rate of population growth vanishes.O C. As the population gets close to the initial population, the rate of population growth vanishes.O D. As the population gets close to carrying capacity, the rate of population growth equals the carrying capacity.

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(1) = 7 A logistic growth model for a certain population with a base population of 5 individuals, carrying capacity individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c). 60 P(t) = 5+7e -0.025 P'(0) a. Is the relative growth in 1999 (t= 0) for the logistic model of the above population equal to r(0) = DVO = 0.015 (rounding to three decimal places)? This would mean that the population was growing at 1.5% per year. Yes O No b. Compute the relative growth rate of the population in 2005 and 2030. What appears to be happening to the relative growth rates as time increases? r(6) =O r(31) = (Round to four decimal places as needed.) What appears to be happening to the relative growth rates as time increases? O A. As time increases, the rate population growth decreases. O B. As time increases, the rate population growth increases. O C. As time increases, the rate of population growth nears the carrying capacity.