Question

the depth of the water, d, in a swimming pool increases and decreases by 3% over a one - month period. match each verbal description of the greatest and least water depths with all equivalent expressions. select the correct button in the table to show which expressions match the verbal description. you may also choose to not select a button for an expression.

	0.97d	1.03d	d - 0.03	d + 0.03d	(1 - 0.03)d
d decreased by 3%

Explanation:

Step1: Analyze "d increased by 3%"

To find the expression for \( d \) increased by 3%, we first convert 3% to a decimal, which is \( 0.03 \). Increasing \( d \) by 3% means we add 3% of \( d \) to \( d \). Mathematically, this is \( d + 0.03d \). We can also factor out \( d \) to get \( d(1 + 0.03)=1.03d \). So the expressions equivalent to " \( d \) increased by 3%" are \( 1.03d \) and \( d + 0.03d \).

Step2: Analyze "d decreased by 3%"

For \( d \) decreased by 3%, we subtract 3% of \( d \) from \( d \). Converting 3% to a decimal gives \( 0.03 \), so the expression is \( d- 0.03d \). Factoring out \( d \), we get \( d(1 - 0.03)=(1 - 0.03)d = 0.97d \). So the expressions equivalent to " \( d \) decreased by 3%" are \( 0.97d \) and \( (1 - 0.03)d \).

Answer:

For " \( d \) increased by 3%":

• \( 0.97d \): Unchecked
• \( 1.03d \): Checked
• \( d - 0.03 \): Unchecked
• \( d + 0.03d \): Checked
• \( (1 - 0.03)d \): Unchecked

For " \( d \) decreased by 3%":

• \( 0.97d \): Checked
• \( 1.03d \): Unchecked
• \( d - 0.03 \): Unchecked
• \( d + 0.03d \): Unchecked
• \( (1 - 0.03)d \): Checked