Question

If agronomists used an exponential model to fit the data, which function h(t), which represents the height of the beanstalk t days after planting, best fits the data? Beans begin to sprout on the 14th day. Consider the value predicted by the model on the 14th day. Which statement is true?

Answer 1

When using GeoGebra, I'm getting the regression curve to be roughly

h(t) = 1.67*(1.4)^t

I'm not sure how your teacher got 1.64 instead of the 1.67, but it's fairly close. So it seems like choice B is the best answer for the first part.

---------------------------------------------------

Once we know the regression equation, we plug in t = 14 to find that,

h(t) = 1.64*(1.4)^t

h(14) = 1.64*(1.4)^(14)

h(14) = 182.236911939151

h(14) = 182.2

If 14 days have gone by, then we estimate the height is roughly 182.2 inches.

Compared to what the table says, which is 190 inches, we see that we have an underestimate. The error is about 190-182.2 = 7.8 which is under 10.

Answer: Choice C

The model under-predicts the actual height by less than 10 inches