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?

Respuesta :

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

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