Safari File Edit View History Bookmarks Window Help 0 webassign.net 88 3. [8/18 Points] DETAILS PREVIOUS ANSWERS MY NOTES A news item is spreading by word of mouth through a population of size 10,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation. 10 y = f (t) = 1 + 150e-0.1t (a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to at least three decimal places.) 0.161 thousand people (b) Calculate the derivative f'(t). 150e0.It f ( t ) = (e0.It + 150 )2 c) At what rate is the news spreading after 8 days? (Give your answer correct to at least four decimal places.) 0.014 thousand people per day (d) Compare the function f(t) to the solutions to the different forms of the logistic growth model from this lesson. Enter the differential equation in terms of y that corresponds to this solution. dy = 0.01y (10 -y) (e) How many people have heard the news when its rate of spread is 0.21 thousand people per day? (There are two answers. Give your answers correct to the nearest whole person.) .93 people (smaller value) people (larger value) th (f) At what two times is the news spreading at rate 0.21 thousand people per day? (Give your answers correct to at least three decimal places.) .5 + days (smaller value) days (larger value) WS (g) What is the fastest rate at which the news spreads? (Give your answer correct to at least three decimal places.) thousand people per day wh 262 96 APR 10webassign.net + 88 2. [-/6 Points] DETAILS MY NOTES The growth of a certain type of weed satisfies a differential equation of the following form, where a is the height of the weed at maturity: dy dt = ky (a - y) Thus we know that the height, y(t), of the weed after t days have passed is given by the following equation: a y (t ) = 1 + Be-akt If a typical weed starts at height 6 centimeters, has height 40 centimeters after 20 days, and reaches height 46 centimeters at maturity, find the values of the constants B and k (correct to at least 4 decimal places). B = K = 3. [8/18 Points] DETAILS PREVIOUS ANSWERS MY NOTES A news item is spreading by word of mouth through a population of size 10,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation. 10 y = f (t) = 1 + 150e-0.1t (a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to atI ' Safari File Edit View History Bookmarks Window Help -" . i ED v ( I] B webassign.net DETAILS PREVIOUS ANSWERS (a) Consider the following logistic growth equation. 1. [GIS Points] : Determine the carrying capacity. (Give an exact answer.) i i g Determine intrinsic growth rate. (Give an exact answer.) i 2 V (b) Consider the following logistic growth. equation. 511- 2 ION 0.0M"? r1! Determine the carrying capacity. (Give an exact answer.) X ' Determine intrinsic grow'dh rate. (Give an exact answer.) EL- 7, V l l l 7 'l l ' 7$Vubn1it