Given:
Initial height of a tree in 1984 = 4 foot
Continuous growth rate =22%
To find:
The height of the tree after 8 years.
Solution:
The general continuous growth model is
[tex]P=P_0e^{rt}[/tex]
Where, [tex]P_0[/tex] is the initial value, r is the growth rate and t is the time in years.
Putting [tex]P_0=4, r=0.22, t=8[/tex] in the above formula, we get
[tex]P=4e^{0.22(8)}[/tex]
[tex]P=4e^{1.76}[/tex]
[tex]P=4(5.81244)[/tex]
[tex]P=23.24976[/tex]
[tex]P\approx 23.25[/tex]
Therefore, the height of the tree after 8 years is 23.25 foot.
