Question

The table shows the number of views of an online video each day.

Day Number of Views
1 100
2 200
3 400
4 800
5 1,600
6 3,200
Model the scenario with an explicit formula and a recursive formula using n for the day and Vn for the number of days.
Explain your reasoning.

Answer 1

The scenario with the online video views can be modeled using an explicit formula Vn = 100 × 2^(n-1) and a recursive formula with V1 = 100 for day 1, and for n > 1, Vn = 2 × V(n-1). These formulas represent exponential growth, where each term is double the previous term.

Step-by-step explanation:

The scenario described in the question shows that the number of views for an online video doubles each day. Given that on day 1 there are 100 views, this relationship can be defined by an exponential growth function.

The explicit formula for the number of views Vn on day n is given by:

Vn = 100 × 2(n-1)

This formula represents an exponential function where the initial value (100 views) is multiplied by 2 raised to the power of one less than the current day number (n-1).

The recursive formula uses the previous day's views to find the current day's views. It can be defined as follows:

For day 1, V1 = 100

For n > 1, Vn = 2 × V(n-1)

Each day's views are twice the previous day's (except the first day which has a defined starting value of 100 views).