Question

A certain forest covers an area of 2600 km2. Suppose that each year this area decreases by 7.75%. What will the area be like after 15 years?

Answer 1

Answer:

After 15 years, the area will be of 775.3 km²

Step-by-step explanation:

The equation for the area of the forest after t years has the following format.

$A(t) = A(0)(1-r)^{t}$

In which A(0) is the initial area and r is the yearly decrease rate.

A certain forest covers an area of 2600 km2.

This means that $A(0) = 2600$

Suppose that each year this area decreases by 7.75%.

This means that $r = 0.0775$

So

$A(t) = 2600(1-0.0775)^{t}$

$A(t) = 2600(0.9225)^{t}$

What will the area be like after 15 years?

This is $A(15)$

$A(t) = 2600(0.9225)^{t}$

$A(15) = 2600(0.9225)^{15} = 775.3$

After 15 years, the area will be of 775.3 km²

Answer 2

Answer:

$A(t) = 2600 (1-0.0775)^t = 2600 (0.9225)^t$

And since the question wants the value for the area at t = 15 years from know we just need to replace t=15 in oir model and we got:

$A(15) = 2600 (0.9225)^{15} = 775.299$

So then we expect about 775.299 km2 remaining for the area of forests.

Step-by-step explanation:

For this case we can use the following model to describe the situation:

$A = A_o (1 \pm r)^{t}$

Where $A_o = 2600 km^2$ represent the initial area

$r =-0.0775$ represent the decreasing rate on fraction

A represent the amount of area remaining and t the number of years

So then our model would be:

$A(t) = 2600 (1-0.0775)^t = 2600 (0.9225)^t$

And since the question wants the value for the area at t = 15 years from know we just need to replace t=15 in oir model and we got:

$A(15) = 2600 (0.9225)^{15} = 775.299$

So then we expect about 775.299 km2 remaining for the area of forests.