You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

47

No worries! We‘ve got your back. Try BYJU‘S free classes today!

56

No worries! We‘ve got your back. Try BYJU‘S free classes today!

61

No worries! We‘ve got your back. Try BYJU‘S free classes today!

71

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $40 t o n s$

Suggest Corrections

Similar questions

Q. The scientists revealed that the amount of pollution emitted to atmophere is 68.2 million tons and by 5 years it will be increased further by 25.73 million tons. What could be the total pollution in the air by the end of 5 years.

Q. The population, P, of Surrey since

1995

can be estimated by the equation

P = 1.0635 x + 3, 250

, where x is the number of years since

1995

and

0 \leq x \leq 20

. In the context of this equation, what does the number

1.0635

most likely represent?

Q. Total greenhouse gas emission

Emission by

6

major sectors Chemical
Industry Air pollution Water pollution Deforestation Fossils Farming

If the total green house gas emission is 24 billion tons a year. What is the amount of greenhouse gas emission from the chemical industry in a year?

On January 1, 2000, there were 175,000 tons of trash in a landfill that had a capacity of 325,000 tons. Each year since then, the amount of trash in the landfill increased by 7,500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?

Q. The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula

C = \frac{100000 p}{100 - p}

. According to this estimate, how much more would it cost to remove

90

percent of the pollutant from the pond than it would cost to remove

80

percent of the pollutant?

Join BYJU'S Learning Program

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.