Renata moved to her new home a few years ago. back then, the young oak tree in her back yard was 190190190 centimeters tall. she measured it once a year and found that it grew at a constant rate. 333 years after she moved into the house, the tree was 274274274 centimeters tall. how fast did the tree grow?

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)

28 cm/year