The table shows the height of a plant over time. Which type of function best models the data? Write an equation to model the data.
year: 0 1 2 3 4
height (cm): 81 101 121 141 161
a. Quadratic; y = 20x^2 + 81
b. Exponential; y = 81 β 20^x
c. Quadratic; y = 81x^2 + 20
d. Linear; y = 20x + 81
please help
so its d. Linear; y = 20x + 81
thank you
goes up by 20 each step
starts at 81
20 x + 81
To determine the type of function that best models the data, we need to analyze the pattern of the height of the plant over time.
From the provided data, we can see that the height increases by 20 cm every year. This linear growth suggests that the function that models the data is linear.
Thus, the correct answer is: d. Linear; y = 20x + 81
To determine the type of function that best models the data, let's examine the pattern in the given table.
Looking at the height values for each year, we can observe that the height increases by a constant amount of 20 centimeters between each consecutive year. This indicates a linear relationship since the increase is constant.
Given this pattern, we can conclude that a linear function best models the data. Now, let's write an equation to represent this linear function.
From the table, we can see that the initial height of the plant, when year (x) is 0, is 81 centimeters. Additionally, we observed that the height increases by 20 centimeters each year (x). Thus, the equation that models the data is:
y = 20x + 81
Therefore, the correct answer is d. Linear; y = 20x + 81.