Question

Determining the Rate of Change Quick Chock 12 ਪੂ The graph shows the height of a tree over time. What can you deduce the rate of change to be from 2 years to 4 years? O 2 inch per year O 2.5 inches per year O 5 inches per year O 10 inches per year 10 co 6 Height (inches) 4 2 X 6 4 5 3 4 2 Time (years) Done Intro ity 远 e here to search​

Answer 1

Consider a tree whose growth is defined by the function

f(t) = t2

t represents time in years,

f (t) represents the height the tree at time t, in feet.

Initially (t = 0), the height of the tree is

f(0) = 02 = 0

After a year (t = 1), the height of the tree becomes

f (1) = 12 = 1

...

For the first five years, we obtain:

f(0) = 02 = 0

f(1) = 12 = 1

f(2) = 22 = 4

f(3) = 32 = 9

f(4) = 42 = 16

f(5) = 52 = 25

Thus

from t = 0 to t = 1, the increase in height is 1 - 0 = 1,

from t = 3 to t = 5, the increase in height is 25 - 9 = 16