Exponential Decay and Functions

This video tutorial explains how to determine an exponential decay function without using logarithms. It uses a real-world example of a radioactive substance decaying over time. The tutorial walks through setting up the function, solving for the base, simplifying the function, and calculating the remaining substance after a given time. The process involves substituting known values, solving for unknowns, and using a calculator for final calculations. The video concludes with a summary of the findings.

What is the initial amount of the radioactive substance?

• 160 milligrams

• 120 milligrams

• 25 milligrams

• 32 milligrams

In the exponential decay function, what does 'a' represent?

• The initial amount

• The remaining amount

• The decay rate

• The time elapsed

What is the ordered pair used to solve for the base 'b'?

• (25, 120)

• (32, 110.7)

• (160, 120)

• (25, 160)

How do you isolate the base 'b' in the equation?

• Subtract 25 from both sides

• Divide both sides by 160

• Divide both sides by 120

• Multiply both sides by 160

What is the significance of the ordered pair (25, 120) in the context of the problem?

• It is irrelevant to the problem

• It shows the remaining amount after 25 hours

• It is used to calculate the decay rate

• It represents the initial amount

What is the simplified form of the exponential decay function?

• p(t) = 160 * (3/4)^(t/25)

• p(t) = 120 * (3/4)^(t/25)

• p(t) = 160 * (4/3)^(t/25)

• p(t) = 160 * (3/4)^t

Why is the base 'b' left in its exact form?

• To avoid rounding errors

• To simplify calculations

• To make it easier to understand

• To increase accuracy

How is the power of 't' expressed in the simplified function?

• t/25

• 25/t

• t*25

• 25^t

What is the purpose of raising both sides to the reciprocal power of 25?

• To find the initial amount

• To calculate the remaining substance

• To solve for 'b'

• To simplify the equation

What is the remaining amount of the substance after 32 hours?

• 120 milligrams

• 110.7 milligrams

• 160 milligrams

• 100 milligrams