The given problem states that the oak tree was growing at a constant rate, therefore the function or equation relating the length of the tree and the years that have passed must take on a linear form:
y = m x + b
where,
y = length of the oak tree
x = number of years
m = the slope of equation / the growth rate
b = the y – intercept / the initial length of the tree = 190 cm
Given already the value of b, the equation becomes:
y = m x + 190
To solve for the value of m, we use another formula:
m = (y2 – y1) / (x2 – x1)
m = (274 – 190) / (3 – 0)
m = 28 cm / year
Therefore the oak tree was growing at a rate of 28 cm per year.
To prove this, we use the equation:
y = 28 x + 190
when x = 3 years
y = 28 (3) + 190
y = 274 cm (TRUE)
Answer:
28 cm/year
