Exploring Decay and Growth Factors in Mathematics

Mario from Mario's Math Tutoring explains the differences between decay factor, decay rate, growth factor, and growth rate using the formula A = P(1 ± R)^T. He provides examples of exponential decay with a car losing value and exponential growth with a classic car gaining value. The video aims to clarify these concepts and help students understand how to apply them in math problems.

What does 'P' represent in the exponential function formula?

• The time in years

• The percentage rate of growth or decay

• The total amount after time 'T'

• The starting amount

How is the rate 'R' used when the quantity is increasing?

• It is multiplied by the time 'T'

• It is divided by the starting amount

• It is added to 1

• It is subtracted from 1

What does the 'T' in the exponential function formula represent?

• Total amount

• Trend line

• Time period

• Transaction number

How do you convert a growth rate from a percentage to a decimal?

• Add 1 to the percentage

• Subtract the percentage from 100

• Multiply by 100

• Divide by 100

What is the correct way to express a 10% growth rate as a decimal?

• 1.1

• 10

• 0.01

• 0.1

What indicates an exponential decay in a function?

• The base of the exponent is greater than 1

• The base of the exponent is 0

• The base of the exponent is less than 1

• The exponent is negative

If a car's value decreases at 20% per year, what is the decay rate in decimal form?

• 2

• 0.2

• 0.8

• 20

In an exponential decay function, what happens to the quantity over time?

• It fluctuates

• It increases without bound

• It remains constant

• It decreases towards zero

What is the growth factor in an exponential growth function?

• The percentage rate of growth

• The total amount after time 'T'

• The quantity in parentheses in the formula

• The starting amount 'P'

How can you identify the decay factor in an exponential function?

• It is the exponent 'T'

• It is the rate 'R' subtracted from 1

• It is the value of 'P'

• It is the quantity inside the parentheses