The growth of a population of rare beetles is given by the logistic function with k=0.00001 and tin months. Assume that there are 200 beetles initially and that the maximum population size is 10,000. a. Find the growth function G(t) for these beetles. Find the population and rate of growth of the population after the following times. b. 7 months C. 4 years d. 6 years e. What happens to the rate of growth over time? a. G(1) = (Type an exact answer in terms of e) b. The population of beetles after 7 months is (Round to three decimal places as needed.) After 7 months, the rate of growth of the population is (Round to three decimal places as needed) beetles per month. C. The population of beetles after 4 years is (Round to three decimal places as needed) beetles. After 4 years, the rate of growth of the population is (Round to three decimal places as needed ) beetles pér month. d. The population of beetles after 6 years is (Round to three decimal places as needed ) beetles.

In 1997, 1500 runners entered a marathon in Joppetown U.S.A. In 2003, 18,000 runners entered the race. Because of the limited number of facilities, the carrying capacity for the number of racers is 58,500. The number of racers at any time, t, in years, can be modeled by the logistic function P(t) = C .Complete parts a) through d) below. %3D 1+Be kt a) What is the value of C? C = b) Find B. B = c) Find k. k = (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.) d) In what year should at least 48,500 runners be expected to run in the race? In the year (Do not round until the final answer Then round un to the nearest whole pumber)

This table is based on a functional relationship between x and y  that is either exponential or a power function: x    y 1    1.8 2    2.07 4    2.38 10   2.85 20   3.28 Use an appropriate logarithmic transformation and a graph to decide wheter the table comes from an exponential function or a power function. Also find the function:      y=

K A meeting of the elders was held in a village in the early 1400's. In the meeting, the date of a future ceremony was first set, and the attendees were instructed to spread the date to their fellow villagers. In the table below, t represents the number of days that had passed since the meeting, and V represents the number of villagers that had acquired the date of the ceremony. t V 2 400 4 608 Logistic y= (y= ₁ + ac-DX) bx 1 ae O B. Linear (y = mx + b) OC. Quadratic (y = ax²+bx+c) OD. Exponential (y=a•b*) 9 1472 16 3024 Use the data to construct a scatter plot, then complete the following. 1) Using the scatter plot and the context of the problem, which of the following best describes the pattern? O A. According to the model, about know the date of the ceremony. 21 3680 Approximately how many villagers were at the meeting of the elders? About villagers were at the meeting. 24 3824 2) Using your calculator and the best of the four methods above, find the model that approximates the…