The video tutorial explains how to create functions to calculate the value of a phone and the number of cells over time. The phone loses 25% of its value annually, and a function is derived to express this depreciation. Similarly, a biologist's sample of cells decreases by one-third weekly due to a virus, and a function is created to model this reduction. Both examples use tables to illustrate the process and derive the functions, emphasizing the pattern of exponential decay.

What is the initial value of the phone when it is sold?

• $500

• $700

• $600

• $800

How much value does the phone retain after one year?

• 75%

• 60%

• 80%

• 50%

What is the value of the phone after two years?

• $600 * 0.75^4

• $600 * 0.75

• $600 * 0.75^2

• $600 * 0.75^3

What is the general formula for the phone's value after t years?

• 600 * 0.9^t

• 600 * 0.25^t

• 600 * 0.5^t

• 600 * 0.75^t

How many cells does the biologist start with?

• 5000

• 6000

• 7000

• 8000

What fraction of cells are killed by the virus each week?

• 1/4

• 1/3

• 1/2

• 2/3

How many cells remain after one week?

• 6000 * 1/3

• 6000 * 1/2

• 6000 * 3/4

• 6000 * 2/3

What is the number of cells after two weeks?

• 6000 * (1/2)^2

• 6000 * (3/4)^2

• 6000 * (1/3)^2

• 6000 * (2/3)^2

What is the general formula for the number of cells after t weeks?

• 6000 * (3/4)^t

• 6000 * (2/3)^t

• 6000 * (1/2)^t

• 6000 * (1/3)^t

What does the function c(t) represent in the context of cell decay?

• The number of cells added each week

• The number of cells remaining after t weeks

• The number of cells killed each week

• The initial number of cells