Question

A city that had 40,000 trees started losing them at a rate of 10 percent per year because of urbanization.

In approximately years, the number of trees in the city reduced to a quarter of the original amount. Hint: Model the situation as P = P0(1 − r)t.

Answer 1

t = 13.1576 years

Explanation:

The situation can be modeled as

P = Po.(1-r)^t

Where

t is the years transcurred

Po is the initial amount

r is the rate of change

Po = 40000

r = 10% equivalent to 0.1

Now

A quarter of the original amount

(1/4)*Po = Po.(1-r)^t

(1/4) = (0.9)^t

t = 13.1576

Please, see attached picture