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1. A hypothetical population has the following population growth parameters: r = 0.4, K=210. a. If the population starts at $N_0$ = 120 at time 0 ($t_0$), calculate the population size for the next five time steps ($t_1$, $t_2$, $t_3$, $t_4$ and $t_5$) assuming exponential and geometric growth. b. If the population starts at $N_0$ = 120 at time 0, calculate the population size for five time steps ($t_1$, $t_2$, $t_3$, $t_4$ and $t_5$), assuming logistic growth. c. On a single set of axes, plot the population size (N) as a function of time for both populations. d. Which of the population trajectories you plotted is a natural population of animals more likely to exhibit? Describe two potential factors might be responsible for this pattern of population gr

          1. A hypothetical population has the following population growth parameters: r = 0.4, K=210.
a. If the population starts at $N_0$ = 120 at time 0 ($t_0$), calculate the population size for the next five
time steps ($t_1$, $t_2$, $t_3$, $t_4$ and $t_5$) assuming exponential and geometric growth.
b. If the population starts at $N_0$ = 120 at time 0, calculate the population size for five time steps
($t_1$, $t_2$, $t_3$, $t_4$ and $t_5$), assuming logistic growth.
c. On a single set of axes, plot the population size (N) as a function of time for both populations.
d. Which of the population trajectories you plotted is a natural population of animals more likely to
exhibit? Describe two potential factors might be responsible for this pattern of population gr

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1. A hypothetical population has the following population growth parameters: r = 0.4, K=210.
a. If the population starts at N0 = 120 at time 0 (t0), calculate the population size for the next five
time steps (t1, t2, t3, t4 and t5) assuming exponential and geometric growth.
b. If the population starts at N0 = 120 at time 0, calculate the population size for five time steps
(t1, t2, t3, t4 and t5), assuming logistic growth.
c. On a single set of axes, plot the population size (N) as a function of time for both populations.
d. Which of the population trajectories you plotted is a natural population of animals more likely to
exhibit? Describe two potential factors might be responsible for this pattern of population gr

Added by Melanie A.

Biology for AP Courses

Julianne Zedalis, John Eggebrecht

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Solved by Expert Joseph Randich

10/10/2022

Step 1

Step 1: Exponential growth: $N_t = N_0e^{rt}$ Geometric growth: $N_t = N_0(1+r)^t$ Logistic growth: $N_{t+1} = N_t + rN_t(1 - \frac{N_t}{K})$ where $N_t$ is the population size at time t, $N_0$ is the initial population size, r is the per capita growth rate, K is Show more…

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1. A hypothetical population has the following population growth parameters: $r = 0.4$, $K=210$. a. If the population starts at $N_0 = 120$ at time 0 ($t_0$), calculate the population size for the next five time steps ($t_1, t_2, t_3, t_4$ and $t_5$) assuming exponential and geometric growth. b. If the population starts at $N_0 = 120$ at time 0, calculate the population size for five time steps ($t_1, t_2, t_3, t_4$ and $t_5$), assuming logistic growth. c. On a single set of axes, plot the population size (N) as a function of time for both populations. d. Which of the population trajectories you plotted is a natural population of animals more likely to exhibit? Describe two potential factors might be responsible for this pattern of population gr

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Transcript

00:01 So here we have a growing population, and the number of individuals is the function of time.

00:07 So n of t is equal to n -0, e to the r t.

00:11 So n -n -n -n -n -stap population time at time.

00:13 Our population size is time 0.

00:15 The constant r is the intrinsic growth rate.

00:17 And in part a, we want to plot a couple functions.

00:20 So part a, we want to draw a plot.

00:24 So in blue, i'm going to draw r equals 2.

00:31 So this, for n equals 100.

00:33 So this is nm t equals 100 e to the 2 t.

00:40 I notice that you cross the axis right here at 100.

00:45 And then in red, i'll draw what happens when we have r equal 3.

00:51 You get something that looks like this.

00:55 So this is 100e to the 3t.

00:59 So it's the same vertical intercept, right? each has the initial population.

01:04 That's equal 0.

01:06 Of a hundred, but the red curve is a little bit steeper.

01:11 So it grows faster, the r equals three grows faster.

01:23 Slightly steeper.

01:26 So then in part b, we're given some values, right? we're given that at time equals zero, and is 100, and the time equals 2, and is 300...

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