Question

It is predicted that the popularity of the hot sauce market will continue to grow in a country. In 2014, hot sauce sales in the country were $1.75 billion. By 2022, sales are expected to be $2.23billion.

a. Assume that the relationship between time, x, and sales of hot sauce in the country, y, is linear and write an equation describing this relationship. Use ordered pairs of the form (years past 2014, sales of hot sauce in billions of dollars).
b. Use this equation to predict sales of hot sauce in the country in the year 2029.

(Type answer in slope intercept form)

Answer 1

(a) y = 0.06x +1.75

(b) $2.65 billion

Explanation:

You want a linear equation relating years after 2014 to hot sauce sales, given sales in 2014 were $1.75 billion, and sales in 2022 were $2.23 billion. And, you want a predicted value for sales in 2029.

Slope

The slope of the linear relation can be found from the points (0, 1.75) and (8, 2.23) using the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (2.23 -1.75)/(8 -0) = 0.48/8 = 0.06

(a) Equation

The first given point is the y-intercept, so we can write the equation as ...

y = mx +b . . . . . where m is the slope and b is the y-intercept

y = 0.06x +1.75

(b) 2029

In 2029, the value of x is 2029 -2014 = 15, so the predicted sales is ...

y = 0.06(15) +1.75 = 0.90 +1.75 = 2.65

The equation predicts sales of $2.65 billion in 2029.

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