Successive Percentage Changes and Multipliers

An item priced at $50 increases by 10% and then decreases by 10%. What is the final price?

$49.50 (Multiply $50 by 1.10 to get $55.00, then multiply $55.00 by 0.90).

A shirt priced at $80 decreases by 20% and then increases by 20%. What is the final price?

$76.80 (0.80 times 1.20 equals 0.96; $80 times 0.96 equals $76.80).

Calculate the single overall multiplier for a 20% increase followed by a 30% increase.

1.56 (Multiply 1.20 by 1.30; this equals an overall increase of 56%, not 50%).

A stock valued at $200 drops by 50% on Monday and rises by 50% on Tuesday. What is its value on Tuesday evening?

$150 (Multiply $200 by 0.50 to get $100, then multiply $100 by 1.50).

A bicycle costs $800. It increases in price by 25% and subsequently drops by 20%. What is the final price?

$800 (Multiply 1.25 by 0.80 to get exactly 1.00; the price returns to its original value).

A savings account with $2,000 earns 4% compound interest annually. Write the expression and calculate the balance after 5 years.

About $2,433.31 (Expression: 2000 * 1.04^5; 1.04 raised to the 5th power is approximately 1.21665).

A patient receives 400 mg of a medication with a half-life of 6 hours. How much medication remains in the blood after 18 hours?

50 mg (18 hours represents 3 half-lives; 400 times (0.5)^3 equals 400 times 0.125, which is 50 mg).