Question

Last year a business earned 4.1 X 10 dollars in income. This year the business eamed 2.05 X 10 dollars in income. Which best describes how this year's earnings compare to last year's earnings?

Answer 1

This year's earnings of 2.05 × 10n dollars represent a 50% decrease from last year's earnings of 4.1 × 10n dollars.

Step-by-step explanation:

Last year, a business earned 4.1 × 10n dollars in income, and this year it earned 2.05 × 10n dollars in income. To determine how this year's earnings compare to last year's, we need to find the percentage change in income. By assuming n is the same for both figures, we can express the change as a percentage decrease in income by using the formula for percentage change, which is ((new value - old value) / old value) × 100%.

Here, the new value is 2.05 × 10n and the old value is 4.1 × 10n. Substituting the values into the formula, we get ((2.05 × 10n - 4.1 × 10n) / 4.1 × 10n) × 100%. This simplifies to ((-2.05 × 10n) / 4.1 × 10n) × 100%, resulting in a percentage change of -50%, indicating a 50% decrease in the business's income from last year to this year.