Question

USING TOOLS The table shows the numbers y (in thousands) of people in a city who regularly use sharable

electric scooters x weeks after the scooters are introduced.
Time, x Number of users, y
1, 1.5
4, 2.2
6, 2.4
10, 3.9
12, 5.5
15, 6.8
20, 12.3
24, 16.4
25, 17.6

1. Write function that models the data

2. Use the model to predict the number of users after 32 weeks

Answer 1

To write a function that models the data, we need to determine the relationship between the independent variable (x) and the dependent variable (y). The function that models the data is y = 0.318x + 1.248. The predicted number of users after 32 weeks is approximately 11,752.

Step-by-step explanation:

To write a function that models the data, we need to determine the relationship between the independent variable (x) and the dependent variable (y). Looking at the given data, we can observe that as the number of weeks after the scooters are introduced (x) increases, the number of users (y) also increases. We can use a linear function to model this relationship:

y = mx + b

where y represents the number of users and x represents the number of weeks after the scooters are introduced. To find the values of m and b, we can use the given data points to solve a system of equations. Taking two points from the given data, let's say (1, 1.5) and (4, 2.2):

1.5 = m(1) + b

2.2 = m(4) + b

Solving this system of equations, we find that m ≈ 0.318 and b ≈ 1.248. Therefore, the function that models the data is:

y = 0.318x + 1.248

To predict the number of users after 32 weeks, we can substitute x = 32 into the function:

y = 0.318(32) + 1.248

y ≈ 11.752

Therefore, the predicted number of users after 32 weeks is approximately 11,752.