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Question 23703: At the age of 8 years, a saguaro cactus is 7 ft tall. After 20 years, the cactus is 10ft tall. Predict the height of the saguaro after 200 years. Assume a linear equation fits the situation to justify your prediction.
8 minus 20 -12
---------------- = ------- = + 4
7 minus 10 - 3
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! I would have made the comparison the other way. I would have determined the rate of change of the height of the cactus compared to the number of years. This would be like the growth measured in feet per year, which is essentially the SLOPE of the line of prediction.
Slope = m = 
In other words, the cactus according to this, the cactus grows 1 foot every 4 years.
Now, find the height when t = 200 years. From 8 years (when it is 7 ft) to 200 years is a difference of 192 years. Every 4 years it grows a foot, so divide 192/4 to get 48 feet, which means that it grew 48 feet over that time. It was already 7 feet, so 7 + 48 = 55 feet tall. That's my final answer!!
Come to think of it, the way you started it off will work as well, except for the sign error that I corrected for you. What you did, you used "years per foot of height" and it gave you a slope of +4 years per foot. That will probably work just as well as what I did.
R^2 at SCC
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