MATH SOLVE

6 months ago

Q:
# 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.

Accepted Solution

A:

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 $100,000β΅ [tex]f(t)=5000e^{0.1t}[/tex]β΅ The total earning = $100,000- Substitute f(t) by 100,000β΄ [tex]100000=5000e^{0.1t}[/tex]- Divide both sides by 5000β΄ [tex]20=e^{0.1t}[/tex]- Insert γ for both sidesβ΄ γ(20) = γ( [tex]e^{0.1t}[/tex] )- Remember γ( [tex]e^{n}[/tex] ) = nβ΄ γ(20) = 0.1 t- Divide both sides by 0.1β΄ t = 29.957β΄ 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