Exponential Growth and Decay Problems

The video tutorial covers various mathematical problems involving exponential growth and decay. It starts with calculating growth factors for bacteria populations over different time intervals, then moves on to city population growth modeling using equations. The tutorial also verifies mathematical statements involving exponents and roots, models city population changes, and calculates substance decay using half-life. Additionally, it compares decay rates of radioactive substances, estimates the value of a sports card over time, and models insect population growth.

If a bacteria population grows by a factor of 1/4 every hour, what is the growth factor for half an hour?

• 1/4

• 1/16

• 1/2

• 1/8

A bacteria population has a growth factor of 3 each hour. What is the growth factor for half an hour?

• 3/2

• 1/3

• √3

• 9

In the equation P(y) = 13,250 * 1.025^y, what does 13,250 represent?

• Population after one month

• Population after one year

• Initial population

• Growth factor per month

Which of the following statements is true?

• 243^(1/3) = √243

• 64^(1/3) = 8

• 15 is a solution to x^2 = 15

• Cube of 27 is a solution to x^3 = 27

What is the growth factor for a city population that changes from 250,000 to 22,500 in one year?

• 1.1

• 0.1

• 1.01

• 0.9

A substance has a half-life of 14 years. How much of the substance is left after 28 years?

• 1/8

• 1/2

• 1

• 1/4

Which substance has a larger initial value if Substance A starts at 100 and Substance B starts at 125?

• Substance B

• Both are equal

• Substance A

• Cannot be determined

What is a reasonable estimate for the value of a sports card after 3 years if it starts at $7 and doubles every 5 years?

• $10.50

• $14

• $21

• $7

By what factor did the insect population increase in the first three weeks if it started at 10 and reached 40?

• 2

• 3

• 4

• 5