20. A gardening store is keeping track of the growth height of different plant types over a month. The table shows the growth height in centimeters for the first, second, third, and fourth weeks.
Week 1 - 12 cm
Week 2 - 18 cm
Week 3 - 24 cm
Week 4 - 30 cm
Which equation represents the relationship between the week number n and the growth height h in centimeters?
a) h = 6n + 6
b) h = 6n - 6
c) h = 6n^2
d) h = 6n/2
To determine the equation that represents the relationship between the week number n and the growth height h in centimeters, we need to analyze the given data.
Looking at the growth heights in the table, we can see that every week the growth increases by 6 centimeters. This implies that for each week, the growth height increases by a constant value of 6 centimeters.
To express this relationship mathematically, we can define a linear equation of the form h = mn + b, where m represents the slope (the constant rate of change) and b represents the y-intercept (the initial or starting point).
Given that the growth height increases by 6 centimeters every week, the slope (m) is equal to 6. The y-intercept (b) corresponds to the initial growth height, which is the height at the start of week 1, given as 12 centimeters.
Substituting the values into the equation, we have h = 6n + 12.
Comparing this equation to the given choices:
a) h = 6n + 6 (Incorrect because the y-intercept is 6, not 12)
b) h = 6n - 6 (Incorrect because the y-intercept is -6, not 12)
c) h = 6n^2 (Incorrect because this is a quadratic equation, not linear)
d) h = 6n/2 (Incorrect because this equation simplifies to h = 3n, not 6n + 12)
Thus, the correct equation that represents the relationship between the week number n and the growth height h in centimeters is:
h = 6n + 12
Therefore, the correct answer is option a) h = 6n + 6.
To determine the relationship between the week number n and the growth height h, we can observe that the growth height increases by 6 cm each week. We can also observe that the growth height starts at 12 cm in the first week.
Using this information, we can deduce that the equation representing the relationship between the week number n and the growth height h is:
h = 6n + 12
Since option a) h = 6n + 6 does not account for the initial height of 12 cm, it can be eliminated as the correct equation.
The correct equation is:
a) h = 6n + 12