The table below shows the average height in feet of trees on a tree farm and a number of years since the trees were planted. Find equation for the function relating the average height and the number of years

Number of years since the trees were planted- |1|3|6|11|15|
Average height(ft)- |10|24|45|80|108|

To find the equation for the function relating the average height and the number of years, we need to determine the pattern or relationship between the two variables. Let's examine the data:

Number of years since the trees were planted - |1|3|6|11|15|
Average height (ft) - |10|24|45|80|108|

Looking at the data, it appears that the average height of the trees increases as the number of years since they were planted increases. To determine the relationship between the average height and the number of years, we can take a closer look at the rate of increase.

Between each consecutive pair of years, we can calculate the difference in average height:

For year 1 to year 3: 24 - 10 = 14
For year 3 to year 6: 45 - 24 = 21
For year 6 to year 11: 80 - 45 = 35
For year 11 to year 15: 108 - 80 = 28

We see that the differences are not constant; they are increasing. This suggests that the relationship between the average height and the number of years is not linear.

Since the differences between the average heights are not constant, we could consider a quadratic or exponential relationship. To determine which relationship is more appropriate, we can plot the data points on a graph and see if they form a linear, quadratic, or exponential curve.

Using the data points provided, we can plot them on a graph. The x-axis represents the number of years since the trees were planted, and the y-axis represents the average height (in feet).

After plotting the points, if they appear to form a straight line, a linear function is most likely appropriate. If they form a curve, we will further investigate whether it is a quadratic or exponential function.

Once the graph is constructed, it will be easier to analyze and determine the equation relating the average height and the number of years.

Note: Without the graph, it is challenging to determine the exact equation relating the average height and the number of years, as there may be multiple possible equations that can fit the data points.

(24-10)/(3-1) = 7

assuming that stays constant, then
y = 7x+3
easy to check.