Question

A bakery sold 3642 pastries in 2010 and 8422 pastries in 2015. Write a linear model that represents the number y of pastries that the bakery sells x years after 2010.

Answer 1

The linear model predicting the number of pastries sold by the bakery x years after 2010 is y = 956x + 3642.

Step-by-step explanation:

To create a linear model that represents the number y of pastries sold by a bakery x years after 2010, we can use two given points: (0, 3642) for the year 2010 and (5, 8422) for the year 2015. The first number in the pair is the number of years since 2010, and the second number is the pastries sold in that year.

First, we calculate the slope (m) of the line:

m = (8422 - 3642) / (5 - 0)
= 4780 / 5
= 956

The slope tells us that the bakery sells an additional 956 pastries each year. Next, we use the y-intercept from the year 2010, which is 3642 pastries when x=0.

Thus, the linear equation representing the annual sales is:

y = 956x + 3642

This model predicts the number of pastries sold x years after 2010.