For each of the past four years, Paulo has grown 2in. every year. He is now 16 years old and 5ft. 10in tall. He figures that when he is 22 years old he will be 6ft 10in. tll. What would you tell Pauo about his conjecture.
I'd say that it's a good start, but he is assuming that his rate of growth will remain the same.
Since there are relatively few people 6'10" tall, it's likely that his extrapolation is too high.
Maybe if he could study the growth rates and heights at various ages of people who did achieve 6'10" height, he would have a sounder basis for his theory.
The pattern sequence and next two terms to 1, 1/4,1/9,1/16,1/25
To verify Paulo's conjecture, let's break down the information and calculate if his growth pattern aligns with his prediction.
We know that Paulo has grown 2 inches each year for the past four years, and he is currently 16 years old and standing at 5ft. 10in.
First, let's calculate how much Paulo has grown in total over the past four years:
2 inches/year * 4 years = 8 inches
Next, let's add the amount he has grown to his current height:
5ft. 10in. + 8 inches = 6ft. 6in.
Based on this calculation, Paulo's current height would be 6ft. 6in., not 6ft. 10in. as he predicted when he turns 22 years old.
Therefore, it seems that Paulo's conjecture may not be accurate. It's important to note that growth patterns can vary, and it is challenging to predict precisely how much someone will grow in the future. Factors such as genetics, nutrition, and overall health can influence growth. It would be best for Paulo to consult with a healthcare professional for a more accurate assessment of his growth potential.
To analyze Paulo's conjecture, we can start by calculating the change in height for each year, based on the information provided.
Since Paulo grew 2 inches each year for the past four years, we calculate his height gain as follows:
4 years * 2 inches/year = 8 inches
Now, let's examine the current height of Paulo, who is 16 years old. He is 5ft 10in tall. In feet and inches, this can be written as:
5ft + 10in = 5ft + (10/12)ft = 5ft + 0.83ft = 5.83ft
If Paulo's conjecture is correct, he believes that when he is 22 years old, he will be 6ft 10in tall. Similarly, we can write this in feet and inches as:
6ft + 10in = 6ft + (10/12)ft = 6ft + 0.83ft = 6.83ft
Now, let's compare the difference between Paulo's current height and his projected height:
Projected height at 22 years = 6.83ft
Current height at 16 years = 5.83ft
Projected height - Current height = 6.83ft - 5.83ft = 1ft
According to this analysis, Paulo's conjecture is incorrect. He is expecting to grow 1 foot from the age of 16 to 22, while he has only grown approximately 8 inches in the past 4 years.