What are the slope and the y-intercept of the linear function that is represented by the table?
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You will need a special formula to compute this.
Years = log (total/principal) / [n * log * (1 + rate / n)]
Part A) Calvin $400 5% monthly 658.80 Time = ?
Monthly compounding "n" = 12
Years = log(658.80/400) / [12 * log(1+ (.05/n))
Years = log ( <span> <span> <span> 1.647 </span> </span> </span> ) / (12 * log ( <span><span><span>1.0041666667 </span> </span> </span> )
Years = 0.21669359917 / 12 * 0.0018058008777
Years = <span> <span> </span></span><span><span>0.21669359917 / 0.0216696105 </span>
</span>Years = <span><span>9.999884362 </span>
</span>
Part B) Makayla 300 6% quarterly 613.04Time=?
Quarterly compounding
n = 4
Years = log (total/principal) / [n * log * (1 + rate / n)]
Years = log (613.04/300) / [4 * log (1 + .06/4)]
Years = log ( <span> <span> <span> 2.0434666667 </span> </span> </span> ) / 4 * log (1.015)
Years = 0.31036755784 / 4 * 0.0064660422492
Years = 0.31036755784 / <span> <span> <span> 0.025864169 </span> </span> </span>
Years = <span> <span> <span> 11.9999044949 </span> </span> </span>
So, the difference is roughly 3 years.
Years = log (total/principal) / [n * log * (1 + rate / n)]
Part A) Calvin $400 5% monthly 658.80 Time = ?
Monthly compounding "n" = 12
Years = log(658.80/400) / [12 * log(1+ (.05/n))
Years = log ( <span> <span> <span> 1.647 </span> </span> </span> ) / (12 * log ( <span><span><span>1.0041666667 </span> </span> </span> )
Years = 0.21669359917 / 12 * 0.0018058008777
Years = <span> <span> </span></span><span><span>0.21669359917 / 0.0216696105 </span>
</span>Years = <span><span>9.999884362 </span>
</span>
Part B) Makayla 300 6% quarterly 613.04Time=?
Quarterly compounding
n = 4
Years = log (total/principal) / [n * log * (1 + rate / n)]
Years = log (613.04/300) / [4 * log (1 + .06/4)]
Years = log ( <span> <span> <span> 2.0434666667 </span> </span> </span> ) / 4 * log (1.015)
Years = 0.31036755784 / 4 * 0.0064660422492
Years = 0.31036755784 / <span> <span> <span> 0.025864169 </span> </span> </span>
Years = <span> <span> <span> 11.9999044949 </span> </span> </span>
So, the difference is roughly 3 years.