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13 Nov 2019
vancements is around 20 billion (estimates range up to 40 billion depending on a number of fac- tors). The estimated world population in 1900 was 1.65 billion and in 2000 it was 6.07 bil- lion. Write world population as a logistic function, P(t), t years after 1900. 62. /Us mo 60. Total sales of a non-brand-name product is likely to follow a logistic model: increasing slowly while the product is relatively unknown, then quickly when it gains popularity, and then slowly again as the product's lifespan is approached. Let the total sales of the product be modeled by the function 0.1t 13e thousand unis, months after its release. (a) Write the formula for S(t) in the form given by the definition. (b) How many units of the product were pre- ordered (which we can model as sales at the moment of its release)? (c) How many units should the producers ex- pect to be sold in the long run? (d) Find and interpret the solution(s) to S(t) = 10 63. (e) An exponential function E(t)- aekt closely follows the graph of the logistic function for small values of t. How different is the solu- tion to E(t) = 10 as compared to S(t) = 10 as computed above? 61. In a paper on chirp rates of a grasshopper (the snowy tree cricket, in particular), the authors mention a formula connecting the rate at which a cricket chirps to the ambient temnerat
vancements is around 20 billion (estimates range up to 40 billion depending on a number of fac- tors). The estimated world population in 1900 was 1.65 billion and in 2000 it was 6.07 bil- lion. Write world population as a logistic function, P(t), t years after 1900. 62. /Us mo 60. Total sales of a non-brand-name product is likely to follow a logistic model: increasing slowly while the product is relatively unknown, then quickly when it gains popularity, and then slowly again as the product's lifespan is approached. Let the total sales of the product be modeled by the function 0.1t 13e thousand unis, months after its release. (a) Write the formula for S(t) in the form given by the definition. (b) How many units of the product were pre- ordered (which we can model as sales at the moment of its release)? (c) How many units should the producers ex- pect to be sold in the long run? (d) Find and interpret the solution(s) to S(t) = 10 63. (e) An exponential function E(t)- aekt closely follows the graph of the logistic function for small values of t. How different is the solu- tion to E(t) = 10 as compared to S(t) = 10 as computed above? 61. In a paper on chirp rates of a grasshopper (the snowy tree cricket, in particular), the authors mention a formula connecting the rate at which a cricket chirps to the ambient temnerat
Sixta KovacekLv2
28 Jul 2019