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Consider an employee's whose earnings, in dollars, are according to the continuous stream f(t)=5,000e0.1t for t>0, where t is measured in years. How many years will it take them to earn a combined total of $100,000? Give your answer in years to the nearest year.

Respuesta :

Ashraf82

It will take him 30 years to earn a combined total of $100,000

Step-by-step explanation:

The earning of an employee represented by the function

[tex]f(t)=5000e^{0.1t}[/tex] , where

  • f(t) is his earning in t years
  • t > 0

We need to find how many years it will take him to earn $100,000

∵ [tex]f(t)=5000e^{0.1t}[/tex]

∵ The total earning = $100,000

- Substitute f(t) by 100,000

∴ [tex]100000=5000e^{0.1t}[/tex]

- Divide both sides by 5000

∴ [tex]20=e^{0.1t}[/tex]

- Insert ㏑ for both sides

∴ ㏑(20) = ㏑( [tex]e^{0.1t}[/tex] )

- Remember ㏑( [tex]e^{n}[/tex] ) = n

∴ ㏑(20) = 0.1 t

- Divide both sides by 0.1

∴ t = 29.957

∴ t = 30 years to the nearest year

It will take him 30 years to earn a combined total of $100,000

Learn more;

You can learn more about the logarithmic functions in brainly.com/question/11921476

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