Respuesta :
Given:
Present number of trees = 2.5 billions
Rate of decrease = 0.5% per month
To find:
The expression that represents how many trees will be left in 10 years?
Solution:
Exponential decay model:
[tex]P(t)=a(1-r)^t[/tex] ...(i)
where, a is initial value, r is decreasing rate and t is time period.
We have,
a = 2.5 billions
r = 0.5% = 0.005 per month
t = 10 years = 120 months [1 year = 12 months]
Putting a=2.5, r=0.005 and t=120 in (i), we get
[tex]P(120)=2.5(1-0.005)^{120}[/tex]
[tex]P(120)=2.5(0.995)^{120}[/tex]
[tex]P(120)=1.3699657[/tex]
[tex]P(120)\approx 1.37[/tex]
Therefore, the required expression is [tex]2.5(1-0.005)^{120}[/tex] and the remaining trees after 10 years is about 1.37 billions.
