Question

The projected equation that models the number of kayaking trips sold an outfitter during the summer is given as y = 28x + 24, where x is the number of weeks since the first week of summer. Due to an advertising campaign atlocal resorts that ended up being more successful than marketers had predicted, the number of trips sold during the first week was 10 more than the predicted number, and the outfitter sold approximately one and a half times the predicted number of trips each week after the first. Which is the best choice for the equation of the line of best fit for the actual number of kayaking trips sold?A) y = 42x + 34B) y = 38x + 36C) y = 42x + 24D) y = 28x + 34

Answer 1

We have to find the equation that fits the number of kayaking trips sold.

We know that the first week 10 more than the predicted value trips were sold in the first week.

The predicted value for the first week (x=0) was yp(0) = 24, so the real value was y(0)=24+10=34.

We also know that after the firste week (x>0), the outfitter sold "one and half" times the predicted value, so we can write this as:

Variation y(x) = 1.5 * Variation yp(x) = 1.5 * Slope yp = 1.5 * 28 = 42

Then, the slope of the actual line is 42.

Then, we can write the equation for the actual y as:

`y=42x+34`

The answer is A) y = 42x + 34