Mastering Geometric Series: Value & Growth Calculations

A car's value depreciates by 20% each year. If the car's initial value is $20,000, what will be its value after 3 years? Identify the geometric series and calculate the total depreciation over the 3 years.

• $12,000 and $8,000

• $15,000 and $5,000

• The value of the car after 3 years is $10,240, and the total depreciation is $9,760.

• $8,000 and $12,000

A company invests $1,000 in a project that yields a return of 10% each year. What will be the total amount after 5 years? Identify the geometric series and calculate the total return.

• 1500.00

• 1610.51

• 2000.00

• 1200.00

A bacteria culture doubles in size every hour. If the initial size is 500 bacteria, how many will there be after 4 hours? Identify the geometric series and calculate the total number of bacteria after 4 hours.

• 8000

• 4000

• 1000

• 2000

A person saves $100 in the first month and increases their savings by 50% each subsequent month. How much will they save in total after 6 months? Identify the geometric series and calculate the total savings.

• 1500.00

• 1200.75

• 1800.50

• 2078.13

A ball is dropped from a height of 80 meters and bounces back to 75% of its height each time. How high will it bounce after the third bounce? Identify the geometric series and calculate the total distance traveled by the ball after 3 bounces.

• 25 meters and 250 meters

• 40 meters and 400 meters

• 50 meters and 500 meters

• 33.75 meters and 323.75 meters

A loan of $5,000 is taken with an interest rate of 5% compounded annually. What will be the total amount owed after 4 years? Identify the geometric series and calculate the total amount.

• 6000.00

• 6077.53

• 5000.00

• 5500.00

A tree grows 30% taller each year. If it is initially 2 meters tall, what will be its height after 3 years? Identify the geometric series and calculate the total growth over the 3 years.

• The height after 3 years is 3.5 meters, with a total growth of 1.5 meters.

• The height after 3 years is 5 meters, with a total growth of 3 meters.

• The height after 3 years is 6 meters, with a total growth of 4 meters.

• The height after 3 years is approximately 4.39 meters, with a total growth of approximately 2.39 meters.

A video game character earns 200 points in the first level and doubles the points earned in each subsequent level. How many points will the character earn after 5 levels? Identify the geometric series and calculate the total points earned.

• 6200

• 8000

• 1200

• 4000

A family plans to save $200 in the first month and increase their savings by 25% each month. How much will they have saved after 8 months? Identify the geometric series and calculate the total savings.

• 1800.00

• 2251.61

• 1500.75

• 2000.50

A phone plan costs $50 in the first month and increases by $5 each month. If the plan continues for 12 months, what will be the total cost? Identify the geometric series and calculate the total expenditure over the year.

• 750

• 900

• 1200

• 600