The height of a plant after each of the first three weeks was 7mm, 20mm, and 33mm, respectively. If this pattern of growth continues, in what week will the plant be more than 100mm tall?
The answer is 9 weeks.
This is what I did, and it's clearly wrong:
tn = 7 + (n-1)13
tn = 7 + 13n - 13
tn = 13n - 6
100 = 13n - 6
100 + 6 = 13n
106/13 = n
I get a crazy decimal (8.1538....) which shouldn't be the answer...
What am I doing wrong, and how do you properly answer this question?
To properly answer this question, let's analyze the pattern of growth:
From the given data, we can see that the height of the plant increases by 13mm each week. In the first week, it grows by 7mm, in the second week by 20mm (which is 7mm + 13mm), and in the third week by 33mm (which is 20mm + 13mm).
To find the number of weeks it takes for the plant to be more than 100mm tall, we need to determine when the plant's height exceeds 100mm.
Let's set up an equation to represent this:
7 + 13n > 100
Here, 'n' represents the number of weeks.
Now, let's solve for 'n':
13n > 100 - 7
13n > 93
Divide both sides by 13:
n > 93/13
To find the next whole number greater than 93/13, we can round up the decimal value of the division. In this case, the next whole number would be 8.
So, it will take 8 weeks for the plant to be more than 100mm tall.
Therefore, the correct answer is 8 weeks, not 9 weeks.