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.

It will take him 30 years to earn a combined total of $100,000Step-by-step explanation:The earning of an employee represented by the function[tex]f(t)=5000e^{0.1t}[/tex] , wheref(t) is his earning in t yearst > 0We 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 $100,000Learn more;You can learn more about the logarithmic functions in brainly.com/question/11921476#LearnwithBrainly