Question

The table shows the circumference of a tree in centimeters, y, at x years.



Choose the function that represents the data.

y =
y = 2.7x
y = 2.7x
y = 2.7x2

Answer 1

I don't see the table in your message. I can pick the correct function, but I need the x and y values.

If you want to check it yourself, here are quick tests you can apply to the table:

1. Linear (y = mx + b)
- Compute the first differences Δy between consecutive y-values.
- If Δy is (approximately) constant, the data are linear. m = that constant; find b by plugging one (x,y).

2. Exponential (y = a·r^x)
- Compute the ratios y_{n+1}/y_n between consecutive y-values.
- If the ratios are (approximately) constant, the data are exponential. r = that constant; a = y when x = 0 (or solve a from any point).

3. Quadratic (y = ax^2 + bx + c)
- If first differences are not constant, compute second differences (differences of the first differences).
- If the second differences are constant, the data are quadratic. Then a = (constant second difference)/2; solve for b and c using two points.

Send the table (or type the pairs x and y) and I’ll identify the model and write the exact formula.