Question

According to the logistic growth equation: $frac{dN}{dt} = rNleft(frac{K - N}{K} ight)$ the number of individuals added per unit time is greatest when N is close to zero. the per capita growth rate (r) increases as N approaches K. population growth is zero when N equals K. the population grows exponentially when K is small. the birth rate (b) approaches zero as N approaches K.

          According to the logistic growth equation:
$frac{dN}{dt} = rNleft(frac{K - N}{K}
ight)$
the number of individuals added per unit time is greatest when N is close to zero.
the per capita growth rate (r) increases as N approaches K.
population growth is zero when N equals K.
the population grows exponentially when K is small.
the birth rate (b) approaches zero as N approaches K.

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$According to the logistic growth equation: fracdNdt = rNleft(fracK - NK ight) the number of individuals added per unit time is greatest when N is close to zero. the per capita growth rate (r) increases as N approaches K. population growth is zero when N equals K. the population grows exponentially when K is small. the birth rate (b) approaches zero as N approaches K.$

Added by Iker D.

Biology for AP Courses

Julianne Zedalis, John Eggebrecht

Instant Answer

Solved by Expert Joanna Quigley

03/15/2022

Step 1

According to the logistic growth equation, the number of individuals added per unit time is not greatest when N is close to zero. Instead, it is greatest when the population size (N) is at half the carrying capacity (K/2). This is because the term (K - N)/K is Show more…

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00:01 According to the logistic growth equation, a, the number of individuals added per unit time is greatest when n is close to zero.

00:09 B, the per capita growth rate increases as n approaches k.

00:14 C, the population growth is zero when n equals k.

00:20 D, the population grows exponentially if k is small.

00:24 Or e, the birth rate b approaches zero as n approaches k.

00:29 So first i'll draw what this actually looks like.

00:34 It gives us this logistic curve.

00:40 So it starts off slow, it becomes rapid, and then as it approaches the carrying capacity, which is k, it slows back down again.

00:47 So k is representing the carrying capacity, and r is representing the per capita growth rate.

01:01 And n is, of course, the population size.

01:04 Okay, so here we have dn over d t.

01:09 So this is t, this is n, and of course it's the gradient.

01:15 So it's highest when the graph is steepest.

01:20 Okay, so which of these is true? let's start with a.

01:22 The number of individuals added per unit time is greatest when n is close to zero.

01:27 Well, no, because that's down here where the gradient is still very low.

01:32 It's not that.

01:33 And that's because of the n, multiplying by.

01:37 The k minus n over k...

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