Question

During the 1990s, the forested area of Guatemala decrelised at an average rate of 1.7%.

If the forested area in Guatemala in 1990 was about 34 400 square kilometers, write an equation for the forested area for t years
after 1990. If this trend continues, predict the forested area in 2015.

Answer 1

The function that represents this situation is f(x) = 34400(0.983)ˣ

The predicted forested area in 2015 is 26598.75 square km

Writing the function that models the situation.

From the question, we have the following parameters that can be used in our computation:

Inital area, a = 34400

Rate of decrease, r = 1.7%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 - r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 34400 * (1 - 1.7%)ˣ

So, we have

f(x) = 34400 * (0.983)ˣ

If this trend continues, predict the forested area in 2015 (t = 15) is

f(15) = 34400 * (0.983)¹⁵

Evaluate

f(15) = 26598.75

Hence, the predicted forested area is 26598.75 square km

Answer 2

A is correct answer

Explanation:

Here, we want to write an equation for a depreciation

The general form is;

V = I( 1 - r)^t

V is the present value in 2015

I is the initial value in 1990 which is 34,400

r is the decrease rate which is 1.7/100 = 0.017

t is the difference in years which is 2015-1990 = 25

Substituting these values, we have

V = 34,400(1-0.017)^25

V = 22,407.65 km^2