Chapter 8.6, Problem LC

(a)

To determine

To calculate: The equation of the best line and the best exponential curve that fits the data representing the ordered pairs $\left(n,a_n\right)$, where $a_n$ represents the number of pennies that are in the cane on the nth dump.

(b)

To determine

To graph: The exponential model, $y=104.1587{\left(0.60691\right)}^x$ and the linear model $y=-6.936x+59.436$ for the number of coins left in the can after the nth dump as obtained in part (a) and interpret which model is better.

(c)

To determine

To calculate: The fraction of pennies that would we placed back into the can after each dump where $a_n$ is the number of pennies dumped after the nth dump.

(d)

To determine

The use of the exponential curve, $y=200{\left(\frac{1}{2}\right)}^x$ for the data assumed in part.

(e)

To determine

To calculate: The number of dumps that were made before there are no pennies left in the can.