Question

when Derek planted a tree it was 36 inches tall the tree grew one and one fourth inches per year the tree is now forty four and three fourths how many years ago did Derek plant the tree

Answer 1

Suppose that the height of the tree is given by exponential growth. This is the given by the form:
y=abˣ
where:
a is the initial value
b is the growth factor
y is the current value
x is the number of years.
From the question:
a=36 in
b=1 1/4=1.25
y=44 3/4=44.75
plugging the values in the equation we get:
44.75=36(1.25ˣ)
solving for x we shall have:
179/144=1.25ˣ
introducing logs
ln(179/144)=x ln 1.25
hence
x=[ln(179/144)]/ln 1.25
x=0.975~ 1 year

Answer: the tree was planted 1 year ago