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Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the diffe
rential equation dPdt=cln(KP)P where c is a constant and K is the carrying capacity. Answer the following questions.
a. Solve the differential equation with a constant c=0.1, carrying capacity K=3000, and initial population P0=1000. Answer: P(t)=
(b) Compute the limiting value of the size of the population. limt→[infinity]P(t)= .(c) At what value of P does P grow fastest? P= .
a. Solve the differential equation with a constant c=0.1, carrying capacity K=3000, and initial population P0=1000. Answer: P(t)=
(b) Compute the limiting value of the size of the population. limt→[infinity]P(t)= .(c) At what value of P does P grow fastest? P= .
1 answer:
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Answer:
11) 153, 85, 238 12) 12, 15, 27
Step-by-step explanation:
To find the area of these shapes, you have to cut them into two seperate shapes as shown the in the image: Shape 1 and Shape 2
11) Let Shape 1 be the rectangle: 17×9=153
let Shape 2 be the triangle: ×10×8.5=42.5×2=85
Total area: 153 + 85 = 238
12) Let cut this shape vertically where you'll have a rectangle thats 3 by 4 and a rectangle that's 5 by 3
Shape 1: 3×4=12
Shape 2: 5×3=15
Total area: 15 + 12 = 27
Answer: c) .
Step-by-step explanation:
Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that
Given function :
Interval : [0,3]
Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that
Since
then, at x=c,
From (i) and (ii), we have
Hence, the correct option is c) .