Step-by-step explanation:
(a) dP/dt = kP (1 − P/L)
L is the carrying capacity (20 billion = 20,000 million).
Since P₀ is small compared to L, we can approximate the initial rate as:
(dP/dt)₀ ≈ kP₀
Using the maximum birth rate and death rate, the initial growth rate is 40 mil/year − 20 mil/year = 20 mil/year.
20 = k (6,100)
k = 1/305
dP/dt = 1/305 P (1 − (P/20,000))
(b) P(t) = 20,000 / (1 + Ce^(-t/305))
6,100 = 20,000 / (1 + C)
C = 2.279
P(t) = 20,000 / (1 + 2.279e^(-t/305))
P(10) = 20,000 / (1 + 2.279e^(-10/305))
P(10) = 6240 million
P(10) = 6.24 billion
This is less than the actual population of 6.9 billion.
(c) P(100) = 20,000 / (1 + 2.279e^(-100/305))
P(100) = 7570 million = 7.57 billion
P(600) = 20,000 / (1 + 2.279e^(-600/305))
P(600) = 15170 million = 15.17 billion
Answer:
30°
Step-by-step explanation:
Answer:
847
Step-by-step explanation:
700 ÷100 = 7
7× 4.2 = 29.4
29.4×5 =147
500+147
Answer:
5
Step-by-step explanation:
45 divided by 9 is 5
For this, you want to find the Factors, the Common ones and then the Greatest of those.
*Always list factor in pairs so that none are missed/left out
First, Factors of 32
1, 32
2, 16
4, 8
Now, Factors of 81
1, 81
3, 27
9
The next step is to highlight/circle the common factors
1,
As there is only one common factor, that is the greatest.
The GCF is 1
