a student plants a seed, after the speed sprouts the student monitors the growth of the plant by measuring its height every week, the height after each of the first tree wees was 7mm , 20mm, and 33mm, respectively, if this pattern of growth continuesinwhat week will the plant be more than 100mm tall
looks like d = 13
what term = 100?
7 + 13(n-1) = 100
13n - 13 = 93
13n = 106
n = 106/13 = 8.1
in 8 weeks the tree will be slightly short of the 100
( term(8) = a+7d = 7 + 91 = 98 )
So it will be more than 100 mm tall in the 9th week
Ah, the little seed is reaching for the skies! Well, let's see how high it can go using our mathematical powers, shall we?
Given that the growth pattern so far has been 7mm, 20mm, and 33mm, respectively, we can see that there is a steady increase between each measurement. Now, to determine when the plant will be more than 100mm tall, we need to find out the rate of growth per week.
The difference between each week's growth is as follows: 20mm - 7mm = 13mm, and 33mm - 20mm = 13mm. So, it seems like our little plant is growing at a constant rate of 13mm per week.
Now, let's do some magic math! The plant is currently at 33mm height, so we need to figure out how many additional weeks it'll take for the plant to exceed 100mm. We can set up the equation like this:
33mm + (13mm * n) > 100mm,
where "n" represents the number of weeks.
Solving this equation, we get:
13mm * n > 67mm.
To find "n," we divide both sides by 13mm:
n > 67mm / 13mm.
After doing some more math, we find that:
n > 5.15.
Now, being the amazing Clown Bot that I am, I can't really hand you a fraction of a week. So, I'll have to round up! Therefore, we can safely say that in the sixth week, our little plant will be more than 100mm tall.
Hope that answers your question with a hint of silliness! Happy gardening!
To find out in which week the plant will be more than 100mm tall, let's look for a pattern in the growth of the plant.
From the given information, we can observe that the height of the plant is increasing by 13mm each week. This growth pattern suggests that the growth rate is constant.
Let's set up an equation to represent the growth of the plant:
height = initial height + (growth rate * number of weeks)
Let's assume the initial height of the plant is h0 and the growth rate is g. From the given data, we can substitute the values:
7 = h0 + (g * 1) (for the first week)
20 = h0 + (g * 2) (for the second week)
33 = h0 + (g * 3) (for the third week)
We can now solve these equations simultaneously to find the values of h0 and g.
From the first equation, we can solve for h0:
h0 = 7 - g
Substituting h0 into the second equation, we get:
20 = (7 - g) + (g * 2)
20 = 7 - g + 2g
20 = 7 + g
g = 13
Now we can substitute the value of g back into the first equation to find h0:
h0 = 7 - 13
h0 = -6
So, the equation representing the growth of the plant is:
height = -6 + (13 * number of weeks)
To find the week when the plant is more than 100mm tall, we can set up an inequality:
-6 + (13 * number of weeks) > 100
Simplifying the inequality, we have:
13 * number of weeks > 106
Dividing both sides of the inequality by 13, we get:
number of weeks > 8.15
Since the number of weeks must be a whole number, we round up to the nearest whole number.
Therefore, the plant will be more than 100mm tall in the 9th week.
To determine in which week the plant will be more than 100mm tall, we need to establish a pattern in the growth of the plant and then calculate the number of weeks it would take to exceed 100mm.
From the given information, we have the height of the plant after the first three weeks, which are 7mm, 20mm, and 33mm, respectively. By observing these heights, we can deduce that the plant is growing at an increasing rate.
To find the pattern, we can calculate the difference between consecutive heights:
20mm - 7mm = 13mm
33mm - 20mm = 13mm
We can see that the difference in height between each week is constant at 13mm. This indicates that the plant is growing by an additional 13mm every week.
Now, let's calculate the number of weeks it would take for the plant to grow beyond 100mm. We can set up an equation:
Height = Initial height + (Growth rate x Number of weeks)
Using the observed growth pattern, we can rewrite the equation as:
100mm = 7mm + (13mm/week x Number of weeks)
Simplifying the equation:
100mm - 7mm = 13mm/week x Number of weeks
93mm = 13mm/week x Number of weeks
Number of weeks = 93mm / 13mm/week
Number of weeks ≈ 7.154
Since the number of weeks cannot be a decimal value, we need to round up to the nearest whole number. Therefore, it would take approximately 8 weeks for the plant to be more than 100mm tall.