Understanding Linear Growth Models

This video tutorial explains how to use recursive and explicit formulas to model linear growth. It provides an example of homes sold over weeks, demonstrating how to calculate the common difference and apply it to write both recursive and explicit formulas. The tutorial concludes by predicting future sales using these formulas.

What is the primary purpose of using recursive and explicit formulas in linear growth models?

• To determine quadratic equations

• To solve logarithmic functions

• To calculate exponential growth

• To model linear growth

In a recursive formula for linear growth, what does 'd' represent?

• The total sum

• The initial amount

• The final value

• The common difference

What is the explicit formula for linear growth?

• P sub n equals d times n

• P sub n equals P sub zero plus d times n

• P sub n equals P sub n minus one plus d

• P sub n equals P sub zero minus d

If four homes were sold in the first week and ten in the second, what is the common difference?

• 4

• 6

• 10

• 14

How do you calculate the common difference 'd' using consecutive weeks' data?

• Multiply P sub zero by P sub one

• Add P sub zero and P sub one

• Subtract P sub zero from P sub one

• Divide P sub one by P sub zero

What is the recursive formula for the number of homes sold in the n+1th week?

• P sub n equals P sub n minus one plus d

• P sub n equals P sub zero plus d times n

• P sub n equals d times n

• P sub n equals P sub zero minus d

In the explicit formula, if P sub zero is 4 and d is 6, what is the formula?

• P sub n equals 4 minus 6 times n

• P sub n equals 6 minus 4 times n

• P sub n equals 4 plus 6 times n

• P sub n equals 6 plus 4 times n

Using the explicit formula, how many homes will be sold in the 5th week?

• 28

• 22

• 24

• 26

Why is it important to remember that the week number is one more than n?

• To avoid confusion in calculations

• To ensure the formula is correct

• To align with the recursive formula

• To match the explicit formula

What is the result of using the explicit formula for n equals 4?

• 32

• 28

• 24

• 20