k$)$ A company that services vending machines considers its income as a continuous stream with an annual rate of flow given by $f(t)=120e^{-0\mathrm{.}4t}$ in thousands of dollars. Find the income from this stream over the next $10$ years. What is the income produced in the last year only? $($Hint: you are not investing the income in this problem$)$

The income over $10$ years is $$294,505.$ The income during only the $9^{th}$ year is $$2,702.$