Question

A certain forest covers an area of 4200km^2 suppose that each year this decreases 8.5% what will the area Be after 5 years

Answer 1

Answer:
`2693.73\ km^2`

Step-by-step explanation:

Given: A certain forest covers an area =
`4200km^2`

The rate of decrease = 8.5 % = 0.085

The exponential decay function is given by :-

`f(t)=A(1-r)^t`, where A is the initial amount , r is the rate of decay and t is the time.

Now, the area after 5 years is given by :-

`f(5)=(4200)(1-0.085)^5\\\\\Rightarrow f(5)=4200(0.915)^5\\\\\Rightarrow f(5)=2693.7343275\approx2693.73\ km^2`

Hence, the area after 5 years =
`2693.73\ km^2`

Answer 2

The correct answer, rounded to the nearest km², is 2694.

Step-by-step explanation:

This can be represented using an exponential equation of the form

y = a(1+r)ˣ, where y is the total amount, a is the initial population, r is the rate of increase or decrease written as a decimal number, and x is the amount of time.

In our problem, a = 4200, r = -8.5% = -8.5/100 = -0.085, and x is 5:

y = 4200(1+-0.085)⁵ = 4200(0.915)⁵ = 2693.73 ≈ 2694.