When Charlotte planted her tomato plant, it grew 3 inches in one week. After 5 weeks, the tomato plant was 23 inches tall. Assume the relationship is linear. Find and interpret the rate of change and the initial value.
It grew 7.66 inches repeating every week.
To find the rate of change and initial value, we need to first understand the relationship between the number of weeks and the height of the tomato plant.
We are given that the tomato plant grew 3 inches in one week. This means that for every week that passes, the height of the plant increases by 3 inches.
Using this information, we can set up a linear equation to represent the relationship between the number of weeks (x) and the height of the tomato plant (y):
y = mx + b
Where:
m = the rate of change (slope)
b = the initial value (y-intercept)
We know that after 5 weeks, the tomato plant was 23 inches tall. So we can substitute these values into the equation to find the values of m and b.
23 = 5m + b
Next, we need to determine the rate of change (m). We can subtract the height of the tomato plant at the beginning (initial value) from the height after 5 weeks and then divide it by the number of weeks:
m = (23 - b) / 5
Since we assume the relationship is linear, the rate of change remains constant over time.
Finally, we can interpret the results. The rate of change (m) represents the amount the height of the tomato plant increases per week. In this case, every week the plant grows by 3 inches.
The initial value (b) represents the starting height of the tomato plant. In this case, it is determined by the equation.