Question

The number of trees in a rainforest decreases each month by 0.5%. The forest currently has 2.5 billion trees. Which expression represents how many trees will be left in 10 years.

Answer 1

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:

$P(t)=a(1-r)^t$         ...(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

$P(120)=2.5(1-0.005)^{120}$

$P(120)=2.5(0.995)^{120}$

$P(120)=1.3699657$

$P(120)\approx 1.37$

Therefore, the required expression is $2.5(1-0.005)^{120}$ and the remaining trees after 10 years is about 1.37 billions.