Each table shows the population of a city over a three-year period. Write an exponential function to represent each population as a function of time.
Understand the Problem
The question asks to write an exponential function that represents the population of a city as a function of time, using data presented in a table (not provided in the image).
Answer
$P(t) = ab^t$
Answer for screen readers
To provide a specific answer, the data tables showing the population of the cities over the three-year period are needed. Without that information, I can only provide the general form of the exponential function:
$P(t) = ab^t$
where: $P(t)$ represents the population at time $t$ $a$ represents the initial population $b$ represents the growth/decay factor $t$ represents the time in years
Steps to Solve
- Identify the general form of an exponential function
An exponential function is generally written as: $y = ab^x$ where: $y$ is the final amount $a$ is the initial amount $b$ is the growth/decay factor $x$ is the time
- Represent population as a function of time
Replace $y$ with $P(t)$ to represent the population $P$ as a function of time $t$
$P(t) = ab^t$
Therefore, to define an exponential function we need to know: the initial population $a$ and the growth/decay factor $b$.
To provide a specific answer, the data tables showing the population of the cities over the three-year period are needed. Without that information, I can only provide the general form of the exponential function:
$P(t) = ab^t$
where: $P(t)$ represents the population at time $t$ $a$ represents the initial population $b$ represents the growth/decay factor $t$ represents the time in years
More Information
The growth/decay factor $b$ can tell us about the population trend. If $b > 1$, the population is growing. If $0 < b < 1$, the population is decreasing. If $b = 1$, the population is not changing.
Tips
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