What does the differential equation dp/dt = K * P represent in the context of exponential growth?

Exponential Growth and Population Modeling

Interactive Video
•
Mathematics, Science
•
9th - 12th Grade
•
Hard

Mia Campbell
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The rate of growth is constant.
The rate of growth is independent of the population.
The rate of growth is inversely proportional to the population.
The rate of growth is proportional to the population.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the solution P(t) = P0 * e^(Kt), what does P0 represent?
The growth rate
The initial population
The constant of integration
The time period
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial population of the town in the example provided?
5,000
4,000
6,000
10,000
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the population after 3 years calculated in the example?
By adding 4% to the initial population
By using the formula P(t) = P0 * e^(0.04 * 3)
By multiplying the initial population by 3
By dividing the initial population by 3
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate population after 3 years according to the example?
5,800
6,000
5,637
5,500
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the formula used to determine the doubling time of a population?
Doubling time = ln(2) / K
Doubling time = 2 * K
Doubling time = K / ln(2)
Doubling time = ln(K) / 2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate doubling time for the population in the example?
10 years
17.3 years
15 years
20 years
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