Answer:
P = 6200 / (1 + 5.2e^(0.0013t))
increases the fastest
Step-by-step explanation:
dP/dt = 0.0013 P (1 − P/6200)
Separate the variables.
dP / [P (1 − P/6200)] = 0.0013 dt
Multiply the left side by 6200 / 6200.
6200 dP / [P (6200 − P)] = 0.0013 dt
Factor P from the denominator.
6200 dP / [P² (6200/P − 1)] = 0.0013 dt
(6200/P²) dP / (6200/P − 1) = 0.0013 dt
Integrate.
ln│6200/P − 1│= 0.0013t + C
Solve for P.
6200/P − 1 = Ce^(0.0013t)
6200/P = 1 + Ce^(0.0013t)
P = 6200 / (1 + Ce^(0.0013t))
At t = 0, P = 1000.
1000 = 6200 / (1 + C)
1 + C = 6.2
C = 5.2
P = 6200 / (1 + 5.2e^(0.0013t))
You need to change the exponent from negative to positive.
The inflection points are where the population increases the fastest.
The answer is zero point four three
You could also write this answer as 0.43
Answer:
You need more information ask the question again but paste a picture
Step-by-step explanation:
Volumes scale as the cube of a corresponding dimension. Therefore, if the radius of a sphere is doubled (r becomes 2r), the surface area becomes 2 squared, or 4 times the original surface area. The volume would become 2 cubed, or 8 times the original volume.
The binomial (2 · x + y)⁷ in expanded form by 128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷.
<h3>How to expand the power of a binomial</h3>
Herein we have the seventh power of a binomial, whose expanded form can be found by using the binomial theorem and Pascal's triangle. Hence, we find the following expression for the expanded form:
(2 · x + y)⁷
(2 · x)⁷ + 7 · (2 · x)⁶ · y + 21 · (2 · x)⁵ · y² + 35 · (2 · x)⁴ · y³ + 35 · (2 · x)³ · y⁴ + 21 · (2 · x)² · y⁵ + 7 · (2 · x) · y⁶ + y⁷
128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷
Then, the binomial (2 · x + y)⁷ in expanded form by 128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷.
To learn more on binomials: brainly.com/question/12249986
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