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Use the equation to find the initial population. Step 1 To find the initial population, substitute t = 1 Therefore, ⇒P(0) = = 1 +26e 1350 -0.95( 1350 Submit Skip (you cannot come back) ) Xin the given solution of the logistic differential equation. Exercise (d) Use the equation to determine when the population will reach 50% of its carrying capacity.

Use the equation to find the initial population. Step 1 To find the initial population, substitute t = 1 Therefore, ⇒P(0) = = 1 +26e 1350 -0.95( 1350 Submit Skip (you cannot come back) ) Xin the given solution of the logistic differential equation. Exercise (d) Use the equation to determine when the population will reach 50% of its carrying capacity.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...
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I need help with this problem i did exercise a and b i need help with exercise c and d please help me

The logistic equation models the growth of a population. 1350 1 +26e7 P(t) = -0.95t Exercise (a) Use the equation to find the value of k. Step 1 All solutions of the logistic differential equation are of the general form L y = 1 + be -kt Hence, compare the solution of the logistic differential equation with the general form of the logistic differential equation to obtain the value of k, k = 0.95 0.95 Exercise (b) Use the equation to find the carrying capacity. Step 1 Again, compare the solution of the logistic differential equation with the general form of the logistic differential equation. Then, obtain the carrying capacity L. ⇒L = 1350 1350
Transcribed Image Text:The logistic equation models the growth of a population. 1350 1 +26e7 P(t) = -0.95t Exercise (a) Use the equation to find the value of k. Step 1 All solutions of the logistic differential equation are of the general form L y = 1 + be -kt Hence, compare the solution of the logistic differential equation with the general form of the logistic differential equation to obtain the value of k, k = 0.95 0.95 Exercise (b) Use the equation to find the carrying capacity. Step 1 Again, compare the solution of the logistic differential equation with the general form of the logistic differential equation. Then, obtain the carrying capacity L. ⇒L = 1350 1350
Exercise (c) Use the equation to find the initial population. Step 1 To find the initial population, substitute t = 1 Therefore, ⇒P(0) Thus, 1 26e Submit Skip (you cannot come back) Exercise (d) Use the equation to determine when the population will reach 50% of its carrying capacity. 1350 Step 1 We want to know when the population will reach 50% of its carrying capacity. 1350 1 +26e-0.95t 1 +26e 1350 -0.95( P(t) 1350 -0.95t Xin the given solution of the logistic differential equation. L 1350
Transcribed Image Text:Exercise (c) Use the equation to find the initial population. Step 1 To find the initial population, substitute t = 1 Therefore, ⇒P(0) Thus, 1 26e Submit Skip (you cannot come back) Exercise (d) Use the equation to determine when the population will reach 50% of its carrying capacity. 1350 Step 1 We want to know when the population will reach 50% of its carrying capacity. 1350 1 +26e-0.95t 1 +26e 1350 -0.95( P(t) 1350 -0.95t Xin the given solution of the logistic differential equation. L 1350
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