Problem $6[$Hint: Unit $5]$ A company expects its rate of annual income during the next three years to grow exponentially at $\backslash (6\backslash \%\backslash )$ per year as follows, which is lower than the market rate of interest of $\backslash (7\backslash \%\backslash )$ : $\backslash [$ f$($t$)=75000$ e$^\{0\mathrm{.}06$ t$\}\backslash ]$ The company would like you to confirm that the accumulated amount of money flow at the end of three years will cover the cost of the machine $($this amount includes the machine cost and interest payments$)$ of $\backslash (\backslash$$ $200,000\backslash ).$ The company is interested in expanding its business and would like to know if there are sufficient earnings to purchase a new machine outright $($without borrowing funds$)$ at $\backslash (\backslash$$ $30,000\backslash ).$ Similarly, find the accumulated amount of money flow that would exist during the next $4$ year period. You predict the following: $-$ The new machine will boost annual income to $\backslash (\backslash$$ $80,000\backslash ),$ and grow exponentially at $\backslash (4\backslash \%\backslash )$ per year for years $4$ through $8.-$ An expected market rate of interest of $\backslash (5\backslash \%\backslash )$ during this time frame. Please advise.