Question
13.
Suppose the population of a town is 2,700 and is growing 4% each year. Write an equation to model the population growth. Predict the population after 12 years.
y = 2,700 ∙ 1.04x; about 4,323 people
y = 4 ∙ 2,700x; about 129,600 people
y = 2,700 ∙ 4x; about 45,298,483,200 people
y = 2,700 ∙ 4x; about 4,323 people
Suppose the population of a town is 2,700 and is growing 4% each year. Write an equation to model the population growth. Predict the population after 12 years.
y = 2,700 ∙ 1.04x; about 4,323 people
y = 4 ∙ 2,700x; about 129,600 people
y = 2,700 ∙ 4x; about 45,298,483,200 people
y = 2,700 ∙ 4x; about 4,323 people
Answers
GPT-4o
The correct equation to model the population growth is:
\[ y = 2700 \cdot 1.04^x \]
where \( y \) is the population after \( x \) years and 2700 is the initial population.
To predict the population after 12 years, substitute \( x = 12 \) into the equation:
\[ y = 2700 \cdot 1.04^{12} \]
First, calculate \( 1.04^{12} \):
\[ 1.04^{12} \approx 1.601032 \]
Then multiply by the initial population:
\[ y \approx 2700 \cdot 1.601032 \approx 4322.7864 \]
So, the population after 12 years is approximately 4,323 people.
Therefore, the correct model and prediction are:
\[ y = 2700 \cdot 1.04^{12}; \text{ about 4,323 people} \]
\[ y = 2700 \cdot 1.04^x \]
where \( y \) is the population after \( x \) years and 2700 is the initial population.
To predict the population after 12 years, substitute \( x = 12 \) into the equation:
\[ y = 2700 \cdot 1.04^{12} \]
First, calculate \( 1.04^{12} \):
\[ 1.04^{12} \approx 1.601032 \]
Then multiply by the initial population:
\[ y \approx 2700 \cdot 1.601032 \approx 4322.7864 \]
So, the population after 12 years is approximately 4,323 people.
Therefore, the correct model and prediction are:
\[ y = 2700 \cdot 1.04^{12}; \text{ about 4,323 people} \]