Question
A company sells a
charcoal grills in 2020. They expect the number of grills sold to increase by 3% each year.
Which equation represents the number of grills, y
, the company expects to sell x
years after 2020?
charcoal grills in 2020. They expect the number of grills sold to increase by 3% each year.
Which equation represents the number of grills, y
, the company expects to sell x
years after 2020?
Answers
GPT-4o mini
To model the number of charcoal grills sold by the company, we can use the formula for exponential growth, which is given by:
\[
y = a(1 + r)^x
\]
Where:
- \( y \) is the number of grills sold after \( x \) years,
- \( a \) is the initial amount of grills sold,
- \( r \) is the growth rate (as a decimal),
- \( x \) is the number of years after 2020.
In this case, the company expects the number of grills sold to increase by 3% each year, so \( r = 0.03 \). Therefore, the equation becomes:
\[
y = a(1 + 0.03)^x
\]
This simplifies to:
\[
y = a(1.03)^x
\]
Here, \( a \) is the number of grills sold in 2020, and \( x \) is the number of years after 2020. If you know the initial number of grills sold in 2020, you can substitute that value for \( a \) to get a specific equation.
\[
y = a(1 + r)^x
\]
Where:
- \( y \) is the number of grills sold after \( x \) years,
- \( a \) is the initial amount of grills sold,
- \( r \) is the growth rate (as a decimal),
- \( x \) is the number of years after 2020.
In this case, the company expects the number of grills sold to increase by 3% each year, so \( r = 0.03 \). Therefore, the equation becomes:
\[
y = a(1 + 0.03)^x
\]
This simplifies to:
\[
y = a(1.03)^x
\]
Here, \( a \) is the number of grills sold in 2020, and \( x \) is the number of years after 2020. If you know the initial number of grills sold in 2020, you can substitute that value for \( a \) to get a specific equation.