Question
The mayor of a city records the population each year since 1980. He models the data as
, where
represents the city's population, in thousands of people, and
represents the number of years since 1980.
Select each true statement based on this population model.
A.
The population was 9,400 people in 1980.
B.
The population was 16,800 people in 1980.
C.
The population has been increasing since 1980.
D.
The population has been decreasing since 1980.
E.
The population has changed by 6% each year since 1980.
F.
The population has changed by 94% each year since 1980.
, where
represents the city's population, in thousands of people, and
represents the number of years since 1980.
Select each true statement based on this population model.
A.
The population was 9,400 people in 1980.
B.
The population was 16,800 people in 1980.
C.
The population has been increasing since 1980.
D.
The population has been decreasing since 1980.
E.
The population has changed by 6% each year since 1980.
F.
The population has changed by 94% each year since 1980.
Answers
GPT-4o mini
To provide accurate insights regarding the statements based on the population model, we need to know the specific form of the model. However, let’s assume a common form for a population growth model, which could be linear or exponential.
1. **If we assume a linear model, it could look something like:**
\[
P(t) = mt + b
\]
where \( P(t) \) represents the population in thousands, \( t \) is the number of years since 1980, \( m \) is the rate of change in population (in thousands per year), and \( b \) is the population at \( t = 0 \) (the year 1980).
- If \( b \) is 9.4, then the population was indeed 9,400 in 1980 (True for statement A).
- If \( b \) is 16.8, then the population was 16,800 in 1980 (True for statement B).
2. **If we assume an exponential growth model, it could look something like:**
\[
P(t) = P_0 e^{rt}
\]
where \( P_0 \) is the initial population at \( t = 0 \) and \( r \) is the growth rate.
- If \( r \) is positive, the population has been increasing since 1980 (True for C).
- If \( r \) is negative, the population has been decreasing since 1980 (True for D).
3. **About the changes in population:**
- A percentage change can be derived from the growth rate \( r \). If \( r \) = 0.06 (6%), then the population changes by 6% each year (True for E).
- If \( r \) = 0.94 (94%), then the population changes by 94% each year (True for F).
Given the absence of the specific population model formula and parameters, here is how you might evaluate the statements you provided:
- A. True if the model indicates 9.4 as the population in thousands.
- B. True if the model indicates 16.8 as the population in thousands.
- C. True if the growth rate is positive.
- D. True if the growth rate is negative.
- E. True if the growth rate is approximately 0.06.
- F. True if the growth rate is approximately 0.94.
If you can provide the actual model or further context, I can give you definitive answers on these statements!
1. **If we assume a linear model, it could look something like:**
\[
P(t) = mt + b
\]
where \( P(t) \) represents the population in thousands, \( t \) is the number of years since 1980, \( m \) is the rate of change in population (in thousands per year), and \( b \) is the population at \( t = 0 \) (the year 1980).
- If \( b \) is 9.4, then the population was indeed 9,400 in 1980 (True for statement A).
- If \( b \) is 16.8, then the population was 16,800 in 1980 (True for statement B).
2. **If we assume an exponential growth model, it could look something like:**
\[
P(t) = P_0 e^{rt}
\]
where \( P_0 \) is the initial population at \( t = 0 \) and \( r \) is the growth rate.
- If \( r \) is positive, the population has been increasing since 1980 (True for C).
- If \( r \) is negative, the population has been decreasing since 1980 (True for D).
3. **About the changes in population:**
- A percentage change can be derived from the growth rate \( r \). If \( r \) = 0.06 (6%), then the population changes by 6% each year (True for E).
- If \( r \) = 0.94 (94%), then the population changes by 94% each year (True for F).
Given the absence of the specific population model formula and parameters, here is how you might evaluate the statements you provided:
- A. True if the model indicates 9.4 as the population in thousands.
- B. True if the model indicates 16.8 as the population in thousands.
- C. True if the growth rate is positive.
- D. True if the growth rate is negative.
- E. True if the growth rate is approximately 0.06.
- F. True if the growth rate is approximately 0.94.
If you can provide the actual model or further context, I can give you definitive answers on these statements!