Question

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.

Answer 1

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

$f(t)=5000e^{0.1t}$ , 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

∵ $f(t)=5000e^{0.1t}$

∵ The total earning = $100,000

- Substitute f(t) by 100,000

∴ $100000=5000e^{0.1t}$

- Divide both sides by 5000

∴ $20=e^{0.1t}$

- Insert ㏑ for both sides

∴ ㏑(20) = ㏑( $e^{0.1t}$ )

- Remember ㏑( $e^{n}$ ) = 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

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

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