Exponential Growth and Decay Problem Solving

Miss Smith's math tutorial covers exponential growth and decay through real-life word problems. The video explains how to use the exponential formula to solve problems involving population growth, juice consumption decline, car depreciation, and bank savings growth. Each example demonstrates how to identify the starting point, rate of change, and time period to calculate the final value. The tutorial emphasizes understanding the context of the problem and correctly interpreting the results.

What is the formula for exponential growth and decay?

• y = a * (b^x)

• y = a / (b^x)

• y = a + bx

• y = a - bx

Tags

CCSS.HSF-IF.C.8B

If a population doubles every 10 years, what is the rate of change (b) in the formula?

• 20

• 0.5

• 2

• 10

Tags

CCSS.HSF-LE.A.1A

What is the population after 50 years if it starts at 3,000 and doubles every 10 years?

• 96,000

• 48,000

• 24,000

• 12,000

What is the value of 'a' in the exponential formula when discussing the initial population of 3,000 people?

• 3,000

• 1.5

• 6,000

• 10

Tags

CCSS.HSF.LE.B.5

How do you convert a percentage to a decimal for use in the exponential formula?

• Divide by 100

• Multiply by 100

• Add 1

• Subtract 1

For a value that depreciates 10% every 6 months, how many periods are there in 7 years?

• 28

• 7

• 10

• 14

What is the approximate amount of juice consumed per person in 2010 if it decreases by 4.1% each year from 16.5 gallons in 1981?

• 4.9 gallons

• 5 gallons

• 16.5 gallons

• 12 gallons

Tags

CCSS.HSF.BF.A.2

How much is a car worth after 7 years if it depreciates 10% every 6 months, starting at $35,000?

• $8,006.88

• $17,500

• $28,000

• $35,000

Tags

CCSS.HSF.BF.A.2

After 12 years, how much money is in Barbara's savings account if it started with $100 and accrues 9% interest annually?

• $281.27

• $200

• $300

• $150

What does 'compounded annually' mean in terms of interest accrual?

• Interest is calculated every 6 months

• Interest is calculated yearly

• Interest is calculated daily

• Interest is calculated monthly