Question

A cupcake shop had $55,000 in sales in the year 1990. In the year 2000, the shop had $105,000 in sales. Assuming a linear relationship, which function models the amount of sales the shop had x years after 1990?

a) \( f(x) = 5000x + 55,000 \)
b) \( f(x) = 5000x + 50,000 \)
c) \( f(x) = 5000x + 60,000 \)
d) \( f(x) = 5000x + 55,000 \)

Answer 1

The function that models the amount of sales the shop had x years after 1990 is f(x) = 5000x + 55,000.

Step-by-step explanation:

To determine the function that models the amount of sales the cupcake shop had x years after 1990, we can use the given data points to find the slope and y-intercept. The sales in 1990 were $55,000 and the sales in 2000 were $105,000. Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values into the equation. The slope is the change in y divided by the change in x, which is (105,000 - 55,000)/(2000 - 1990) = 5000. The y-intercept is the value of y when x = 0, which is 55,000. Therefore, the function that models the amount of sales the shop had x years after 1990 is f(x) = 5000x + 55,000.