Question

1. deforestation during the 1990s, the forested area of guatemala decreased 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.

Explanation:

Step1: Define decay model formula

This is exponential decay, so use $A(t) = A_0(1-r)^t$, where $A_0$ is initial area, $r$ is decay rate, $t$ is time in years.

Step2: Plug in known values

$A_0 = 34400$, $r = 0.017$, so substitute:
$A(t) = 34400(1-0.017)^t = 34400(0.983)^t$

Step3: Calculate $t$ for 2015

$t = 2015 - 1990 = 25$

Step4: Compute 2015 forested area

Substitute $t=25$ into the equation:
$A(25) = 34400(0.983)^{25}$
First calculate $(0.983)^{25} \approx 0.659$
Then $A(25) \approx 34400 \times 0.659 \approx 22670$

Answer:

Equation for forested area: $A(t) = 34400(0.983)^t$
Forested area in 2015: Approximately 22,670 square kilometers