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Standard IX

Biology

Harmful Effects of Solid Wastes

Pollution is ...

Question

Pollution is being removed from a lake at a rate modeled by the function $y = 20 e^{- 0.5 t}$ tons/yr, where $t$ is the number of years since $1995$ . Estimate the amount of pollution removed from the lake between $1995$ and $2005$ . Round your answer to the nearest ton.

40

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47

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56

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61

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71

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Solution

The correct option is A $40$
Given : pollution removal rate $y = {20 e}^{- 0.5 t}$
Where $t =$ number of years since $1995$
Amount of pollution removed from the lake between $1995$ and $2005$
Amount $= \int_{1995}^{2015} y d x = 20 \int_{1995}^{2005} [e^{- 0.5 t}] d t$
$A = \frac{20}{- (0.5)} [{[e^{- 0.5 t}]}_{1995}^{- 0.5 t}] A = - 40 [e^{- (0.5) (2015)} - e^{- (0.5) (1995)}] A = + 40 [\frac{1}{e^{997.8}} - \frac{1}{e^{1007.5}}] A = 40 t o n s$
Hence the correct answer is $40 t o n s$

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Pollution is being removed from a lake at a rate modeled by the function y=20e−0.5t tons/yr, where t is the number of years since 1995. Estimate the amount of pollution removed from the lake between 1995 and 2005. Round your answer to the nearest ton.

Pollution is being removed from a lake at a rate modeled by the function $y = 20 e^{- 0.5 t}$ tons/yr, where $t$ is the number of years since $1995$ . Estimate the amount of pollution removed from the lake between $1995$ and $2005$ . Round your answer to the nearest ton.