Question Help The total expenditures (in millions) of current dollars for pollut

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Question Help The total expenditures (in millions) of current dollars for pollution abatement and control during the period from 2000 through 2019 can by the function be P(x) = 167.74 e 0.05x, where x = 0 corresponds to the year 2000. (a) In what year would the total expenditures reach $217 million dollars? (b) If this model remains accurate, when would the total expenditures reach $481 million? (a) The expenditures would reach $217 million in the year early- Simplify your answer. Type a whole number.) Enter your answer in the answer box and then click Check Answer OK

Explanation / Answer

P(x) = 167.74 e0.05x

(a) When P(x) = 217

=> 217 = 167.74 e0.05x

=> e0.05x = 217 / 167.74

=> 0.05x = ln (217 / 167.74)

=> x = ln (217 / 167.74) / 0.05

=> x = 5.1496

x = 6 is the year it will actually reach $217 million.

The expenditure would reach $127 million in the year 2006.

(b) When P(x) = 481

=> 481 = 167.74 e0.05x

=> e0.05x = 481 / 167.74

=> 0.05x = ln (481 / 167.74)

=> x = ln (481 / 167.74) / 0.05

=> x = 21.0690

x = 22 is the year it will actually reach $481 million.

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