Exponential Growth and Decay

Solve the exponential decay problem: A radioactive substance has a half-life of 20 days. If there are 100 grams initially, how much will be left after 60 days?

• 10 grams

• 25 grams

• 12.5 grams

• 50 grams

Identify the growth factor in the exponential function y = 2 * (1.05)^x

• 1.05

• 0.05

• 1.5

• 2

Identify the decay factor in the exponential function y = 500 * (0.8)^x

• 0.8

• y = 500

• x

• 500

Apply exponential growth in a real-life scenario: A population of bacteria doubles every hour. If there are 100 bacteria initially, how many will there be after 5 hours?

• 1000

• 500

• 3200

• 2000

Apply exponential decay in a real-life scenario: A radioactive substance decays at a rate of 3% per year. If there are 500 grams initially, how much will be left after 10 years?

• The amount remaining after 10 years will be approximately 500 * 0.7374 = 368.7 grams.

• The amount remaining after 10 years will be exactly 500 * 0.7 = 350 grams.

• The amount remaining after 10 years will be approximately 500 * 0.97 = 485 grams.

• The amount remaining after 10 years will be exactly 500 * 0.3 = 150 grams.

Solve the exponential decay problem: A certain medication decreases in strength by 10% each hour. If there are 200 milligrams initially, how much will be left after 5 hours?

• 100 mg

• 118.098 mg

• 150 mg

• 180 mg

Identify the growth factor in the exponential function y = 3 * (1.2)^x

• 3

• 1.5

• 2

• 1.2

Identify the decay factor in the exponential function y = 800 * (0.9)^x

• 800

• 0.9

• y = 800

• x

Apply exponential growth in a real-life scenario: A savings account earns 4% interest compounded annually. If $1000 is deposited initially, how much will be in the account after 10 years?

• $1300.60

• $1200.40

• $1480.24

• $1400.80

Apply exponential decay in a real-life scenario: The value of a car depreciates by 15% each year. If the car is initially worth $20,000, how much will it be worth after 5 years?

• $10,500

• $12,000

• $8,240.10

• $7,800