Exponential Growth and Decay Word Problems Mastery

The video tutorial covers exponential growth and decay through two word problems. The first problem involves calculating the remaining percentage of a radioactive substance after a certain time, using a decay rate of 3.5% per hour. The second problem examines the growth of a fast food chain, increasing at a rate of 8% annually, to determine the number of stores after several years. The tutorial explains the use of exponential formulas to solve these problems, emphasizing the concept of compounding growth and decay.

What is the percentage of a radioactive substance left after 1 hour if it decays at 3.5% per hour?

• 3.5%

• 100%

• 93.5%

• 96.5%

After 6 hours, what percentage of the radioactive substance remains?

• 96.5%

• 75%

• 80.75%

• 83.5%

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CCSS.HSF.LE.A.4

What is the initial number of stores Nadia's fast food chain had in 1999?

• 150

• 250

• 300

• 200

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CCSS.HSF.LE.B.5

What is the annual growth rate of Nadia's fast food chain?

• 12%

• 5%

• 8%

• 10%

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CCSS.HSF-LE.A.1C

How many stores does Nadia's fast food chain operate in 2000?

• 200

• 208

• 214

• 216

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CCSS.HSF.IF.A.2

What is the common ratio used to calculate the growth of Nadia's fast food chain?

• 1.10

• 1.08

• 1.05

• 1.02

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CCSS.HSF.BF.A.2

How many stores will Nadia's chain operate after 2 years from 1999?

• 216

• 224

• 232

• 208

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CCSS.HSF.BF.A.2

What is the formula to calculate the number of stores operated by Nadia's chain after n years?

• 200 * 1.08^n

• 200 + (0.08 * n)

• 200 * (1 + 0.08)^n

• 200 * (1 - 0.08)^n

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CCSS.HSF.BF.A.2

In what year is Nadia's fast food chain operating 370 stores?

• 2010

• 2009

• 2007

• 2005

How does exponential growth affect the number of stores in Nadia's fast food chain over 8 years?

• It doubles the number of stores.

• It slightly increases the number of stores.

• It results in a dramatic increase in the number of stores.

• It has no significant effect on the number of stores.