Answer :
To model the sales of the magazine based on the given information, we need to understand how the sales increase over the years.
1. Initial Sales: The publisher sold 29,000 copies in the first year.
2. Sales Increase: The sales are expected to increase by 7% each year. This means that each year, sales will be 107% (which is 100% of the original amount plus an additional 7%).
3. Equation Setup:
- In the first year, sales are 29,000 copies.
- In the second year, sales will be 29,000 times 1.07 (because of a 7% increase).
- In the third year, sales will be 29,000 times 1.07 squared (a 7% increase applied again).
- This pattern continues, which leads to geometric growth.
4. General Model: The sales in any given year, [tex]\( x \)[/tex], after the first year can be calculated as:
[tex]\[
y = 29000 \times (1.07)^x
\][/tex]
Here, [tex]\( y \)[/tex] is the expected sales, and [tex]\( x \)[/tex] is the number of years after the first year.
So, the equation that models this situation correctly is:
- D. [tex]\( y = 29000 \times (1.07)^x \)[/tex]
This equation includes a base amount of 29,000 and iteratively multiplies it by 1.07 for each year after the first to account for the expected 7% annual increase.
1. Initial Sales: The publisher sold 29,000 copies in the first year.
2. Sales Increase: The sales are expected to increase by 7% each year. This means that each year, sales will be 107% (which is 100% of the original amount plus an additional 7%).
3. Equation Setup:
- In the first year, sales are 29,000 copies.
- In the second year, sales will be 29,000 times 1.07 (because of a 7% increase).
- In the third year, sales will be 29,000 times 1.07 squared (a 7% increase applied again).
- This pattern continues, which leads to geometric growth.
4. General Model: The sales in any given year, [tex]\( x \)[/tex], after the first year can be calculated as:
[tex]\[
y = 29000 \times (1.07)^x
\][/tex]
Here, [tex]\( y \)[/tex] is the expected sales, and [tex]\( x \)[/tex] is the number of years after the first year.
So, the equation that models this situation correctly is:
- D. [tex]\( y = 29000 \times (1.07)^x \)[/tex]
This equation includes a base amount of 29,000 and iteratively multiplies it by 1.07 for each year after the first to account for the expected 7% annual increase.
