Exponential Growth User Calculations

The video tutorial explains how to calculate the growth of a social media site's user base, which increases by 47% each month. Starting with 50,000 users, the tutorial guides viewers through setting up a calculation table, analyzing user growth month by month, and deriving the correct mathematical expression to represent the total number of new users added over a year. The tutorial emphasizes understanding the pattern of growth and selecting the correct expression from given options.

What was the initial number of users on January 1st of last year?

• 10,000

• 25,000

• 50,000

• 100,000

By what percentage did the user base increase each month?

• 25%

• 47%

• 75%

• 50%

How do you calculate the number of users at the end of the first month?

• Add 47%

• Subtract 47%

• Multiply by 1.47

• Divide by 1.47

What is the expression for the number of users at the end of the second month?

• 50 * 1.47^4

• 50 * 1.47^3

• 50 * 1.47^2

• 50 * 1.47

In the third month, what power of 1.47 is used to calculate the users?

• 4

• 1

• 2

• 3

What is the general formula for the number of users at the start of the nth month?

• 50 * 1.47^n

• 50 * 1.47^(n-1)

• 50 * 1.47^(n+1)

• 50 * 1.47^(n-2)

How do you calculate the new users added in the nth month?

• Subtract 0.47

• Add 0.47

• Multiply by 0.47

• Divide by 0.47

What is the expression for the total new users added through month n?

• 50 * 1.47^n - 50

• 50 * 1.47^n + 50

• 50 * 1.47^n * 50

• 50 * 1.47^n / 50

What common factors are factored out in the alternative method?

• 0.47 and 50

• 1.47 and 50

• 1.47 and 100

• 0.47 and 1.47

Which expression matches the alternative method's result?

• First expression

• Second expression

• Third expression

• Fourth expression