Question

The number of acres in a landfill is given by the function A = 2100e -0.05t , where is measured in years. Use the following graph to approximate, to the nearest hundred, how many acres will the landfill have after 20 years and 40 years?

Answer 1

Answer:

Given that:

The number of acres in a landfill is given by the function

$A = 2100e^{-0.05t}$

where, t is measured in years.

We have to find how many acres will the landfill have after 20 years and 40 years.

For t = 20 years.

$A = 2100e^{-0.05 \cdot 20}$

$A = 2100e^{-1}$

Simplify:

$A = 772.546826$

Similarly, for t = 40 years

$A = 2100e^{-0.05 \cdot 40}$

$A = 2100e^{-2}$

Simplify:

$A = 284.204095$

Therefore, the acres will the landfill have after 20 years and 40 years to the nearest hundredth are, 772.55 and 284.21