Question

Given the expression 75 · (1 – 0.20)2x, determine the percent rate of change.

Answer 1

The expression 75 · (1 – 0.20)2x represents a 20% decrease each time it is applied, but without additional context, such as the value of 'x', a precise percent rate of change cannot be determined. This type of repeated decrease is similar to compound interest calculations.

Step-by-step explanation:

The student is asking to determine the percent rate of change for the expression 75 · (1 – 0.20)2x. To find the percent rate of change, we firstly need to recognize that the expression inside the parentheses represents a percentage decrease, specifically a 20% decrease, since 1 – 0.20 = 0.80 or 80% of the original amount. We can ignore the coefficient of 75 for the moment, focusing on the rate of change.

The rate of change expressed as a percentage is normally calculated using the formula Percentage change = (Change in quantity / Original quantity) × 100. In this case, the original quantity can be thought of as '1' or 100%, and the change in quantity is '1 – 0.80' or '0.20'. Plugging these values into the formula would typically give us a 20% decrease. However, because the decrease is occurring multiple times, as indicated by the exponent2x, this represents a repeated rate of change, or a repeated decrease, not just a single occurrence.

Therefore, without additional context, such as the value of 'x' or how the expression is applied over time (e.g., compounded annually, monthly, etc.), we cannot calculate a precise percent rate of change. In real-world terms, this formula might be akin to calculating the effective interest rate of a loan or investment when there is compounding involved. As probabilities or percent rate of change are calculated in similar ways, one must consider these aspects before drawing a definitive conclusion.

Answer 2

The correct option is c. -36%.

Let's go through the steps:

1. Calculate the original expression:

`\[75 \cdot (1 - 0.20)^2\]`

2. Simplify the expression:

`\[75 \cdot (0.80)^2\]`

3. Calculate the result:

`\[75 \cdot 0.64 = 48\]`

4. Determine the percent change:

`\[ \text{Percent Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) * 100\] \[ \text{Percent Change} = \left( (48 - 75)/(75) \right) * 100\]\\`
5. Simplify the percent change:

`\[ \text{Percent Change} = \left( (-27)/(75) \right) * 100 = -36\%\]\\`

Complete question:-

Given the expression 75 · (1 – 0.20)²× , determine the percent rate of change. a. 80% b. 64% c. -36% d. 20%