Final answer:
The function to express the price in terms of ounces is f(x) = 0.018x + 0.18. A 52 oz. can according to the model should cost $1.116, so at $1.39, it is overpriced. An individual serving can costing $0.21 should contain about 1.67 ounces.
Step-by-step explanation:
To write a function that expresses the price in terms of the number of ounces in a can, we need to find the rate of change in price with respect to the weight. We are given two points: (23, 0.63) and (15, 0.45), where the first coordinate is the weight in ounces and the second coordinate is the price in dollars. Using the formula for the slope, m = (y2 - y1) / (x2 - x1), the slope m is (0.63 - 0.45) / (23 - 15), which gives us 0.018 dollars per ounce. Now we can use one of the points to find the y-intercept (b) in the equation y = mx + b. Using the point (15, 0.45), 0.45 = (0.018)(15) + b, we find that b = 0.45 - (0.018)(15), which gives us a y-intercept of 0.18. Hence, the function is f(x) = 0.018x + 0.18.
To determine if the 52 oz. can is over-priced or under-priced according to the model, we evaluate f(52) = 0.018(52) + 0.18, which equals $1.116. Since the actual price is $1.39, the can is overpriced based on our model.
Lastly, to find the weight of green beans you would expect in an "individual serving" can that costs $0.21, we solve the equation 0.018x + 0.18 = 0.21. Subtracting 0.18 from both sides gives us 0.018x = 0.03, so x = 0.03 / 0.018, which is approximately 1.67 ounces; therefore, we would expect about 1.67 ounces in a serving can.