Question

A population size at t=0 is 80 and has a growth rate of 0.12. If the population follows logistic growth, what is the growth rate constant if the carrying capacity is 240. (1) 5.32(2) 9.60,(3)0.18(4)3.80​

Answer 1

Answer:

Explanation:

"The basic growth rate is expressed as the variation between two different values in time exactly on the behalf of the percentage of the initial value. The general formula of growth rate is given below.

Growth rate = (present value – past value) / past value

If the carrying capacity is 240, then the growth rate constant is 3.80."

Answer 2

Explanation:

The population growth rate (exponential) is expressed as:

dN/dt = rN. --------------- (1)

where,

r= growth rate

N= population size

and dN/dt = growth rate of population in a given instant.

Here, r= 0.12 and N=80

So, dN/dt = 0.12 * 80 = 9.6

Now, it is given that if the population follows logistic growth, then this formula comes into picture:

dN/dt = rN (1-N/k). ------------- (2)

where, k is the carrying capacity.

And, we need to find new r (growth rate constant)

Putting values in equation 2

9.6 = r * 80 (1- 80/240)

9.6 = r * 80 (160/240)

9.6 * 3/160 = r

r= 0.18

So, answer is C.