Answer:
Given that:
The number of acres in a landfill is given by the function
[tex]A = 2100e^{-0.05t}[/tex]
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.
[tex]A = 2100e^{-0.05 \cdot 20}[/tex]
[tex]A = 2100e^{-1}[/tex]
Simplify:
[tex]A = 772.546826[/tex]
Similarly, for t = 40 years
[tex]A = 2100e^{-0.05 \cdot 40}[/tex]
[tex]A = 2100e^{-2}[/tex]
Simplify:
[tex]A = 284.204095[/tex]
Therefore, the acres will the landfill have after 20 years and 40 years to the nearest hundredth are, 772.55 and 284.21