Question

The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*t, where t is the number of years since a government program was began to help clean up the lake. About how long will it take for the amount of pollutant to reach 7 parts per million?

Answer 1

Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.

What is the exponential function for the amount of the substance?

It is given by, after t years:

$A(t) = 14(2.71)^{-0.016t}$

It will reach an amount of 7 parts per million when A(t) = 7, hence:

$A(t) = 14(2.71)^{-0.016t}$

$7 = 14(2.71)^{-0.016t}$

$(2.71)^{-0.016t} = 0.5$

$\log{(2.71)^{-0.016t}} = \log{0.5}$

$-0.016t\log{(2.71)} = \log{0.5}$

$t = -\frac{\log{0.5}}{0.016\log{2.71}}$

t = 43.5.

More can be learned about exponential functions at brainly.com/question/25537936

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