An underground storage container is leaking a toxic chemical. One year after the leak began, the chemical had spread 1500 meters from its source. After two years, the chemical had spread 900 meters more, and by the end of the third year, it had reached an additional 540 meters. If this pattern continues, how far will the spill have spread from its source after 10 years? a. 2775 meters c. 3727 meters b. 3750 meters d. 2940 meters

c. 3727 meters

Step-by-step explanation:

Given;

the chemical had spread 1500 meters from its source.

At n=1, x1 = 1500 m

After two years, the chemical had spread 900 meters more.

At n=2, x2 = 900 m

and by the end of the third year, it had reached an additional 540 meters

At n = 3, x3 = 540 m

The chemical spread for the three years can be used to form a geometric progression G. P.

First term a = x1 = 1500 m

Common ratio r = x2/x1 = 900/1500 = 0.6

number of terms n = 10 years

Sum of nth term of a GP;

S (n) = a (1 - r^n) / (1 - r) (since r < 1)

Substituting the given values;

S (10) = 1500 (1-0.6^10) : (1-0.6)

S (10) = 3727.325184 = 3727 meters

After 10 years it would have spread 3,727 meters