Solving Exponential Growth and Decay Problems

This video tutorial covers solving exponential growth and decay problems through various examples. It begins with an introduction to exponential equations, followed by practical problems involving rabbit population growth, car depreciation, home value appreciation, and bacteria population growth. The video explains how to use exponential formulas and logarithms to solve these problems, providing step-by-step solutions and calculations.

What is the formula for exponential growth?

• y = a + b^x

• y = a * (1 - r)^t

• y = a * (1 + r)^t

• y = a / (1 + r)^t

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CCSS.HSF-IF.C.8B

By what percentage does the rabbit population increase annually?

• 10%

• 8%

• 5%

• 12%

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CCSS.HSF-LE.A.1C

What is the formula used for exponential decay?

• y = a - b^x

• y = a * (1 + r)^t

• y = a * (1 - r)^t

• y = a / (1 - r)^t

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CCSS.HSF-LE.A.1A

How much will the car be worth in 2024?

• $22,500.00

• $20,816.44

• $18,000.00

• $19,250.00

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CCSS.HSF.BF.A.2

What is the percentage increase in the value of the home each year?

• 3%

• 4%

• 5%

• 6%

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CCSS.HSF-LE.A.1C

How much did John pay for his home in 2002?

• $135,129.17

• $150,000.00

• $125,000.00

• $140,250.00

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CCSS.HSF.BF.A.2

How many times does the bacteria double in an hour?

• 5 times

• 2 times

• 3 times

• 4 times

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CCSS.HSF.LE.A.4

How many counts of bacteria will there be in three hours?

• 600,000 counts

• 512,000 counts

• 450,000 counts

• 500,000 counts

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CCSS.HSF.LE.A.4

How long will it take for the sample to contain 500 million counts of bacteria?

• 2.75 hours

• 3.51 hours

• 4.00 hours

• 5.00 hours

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CCSS.HSF.LE.A.4

What is the growth factor when the bacteria triples?

• 4

• 2

• 5

• 3

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CCSS.HSF-IF.C.8B