Podcast
Questions and Answers
The population $P$, measured in millions, of a city in $t$ years' time is modeled by the equation $P = 5e^{0.04t}$. What is the present (initial) population of the city?
The population $P$, measured in millions, of a city in $t$ years' time is modeled by the equation $P = 5e^{0.04t}$. What is the present (initial) population of the city?
5 million
The population $P$, measured in millions, of a city in $t$ years' time is modeled by the equation $P = 5e^{0.04t}$. What is the population of the city after six years, correct to 3 significant figures?
The population $P$, measured in millions, of a city in $t$ years' time is modeled by the equation $P = 5e^{0.04t}$. What is the population of the city after six years, correct to 3 significant figures?
6.35 million
The population $P$, measured in millions, of a city in $t$ years' time is modeled by the equation $P = 5e^{0.04t}$. Sketch the graph of the equation $P = 5e^{0.04t}$ to illustrate the population growth.
The population $P$, measured in millions, of a city in $t$ years' time is modeled by the equation $P = 5e^{0.04t}$. Sketch the graph of the equation $P = 5e^{0.04t}$ to illustrate the population growth.
The graph should show an exponential curve starting at (0, 5) and increasing as t increases.
Flashcards
Initial Population
Initial Population
The population at time t=0.
Finding Population at a Specific Time
Finding Population at a Specific Time
Substitute the given time (t) into the population equation.
Exponential Growth Graph
Exponential Growth Graph
A curve that shows exponential increase over time.
Population Growth Formula
Population Growth Formula
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Time Axis in Growth Model
Time Axis in Growth Model
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Population Axis in Growth Model
Population Axis in Growth Model
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What is 'e'?
What is 'e'?
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Growth Rate
Growth Rate
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Significant Figures
Significant Figures
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Initial Value
Initial Value
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Study Notes
- The population P, measured in millions, of a city in t years' time is modeled by the equation P = 5e^0.04t.
Task List
- Determine the initial population of the city.
- Calculate the population of the city after six years, rounded to three significant figures.
- Sketch the graph of P = 5e^0.04t to represent the population growth.
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Description
This lesson explores an exponential model for population growth. It involves finding the initial population, calculating future population size, and graphically representing the growth model.
