A dry cleaner uses exponential smoothing to forcast equipment usage at its plant. August usage was forcasted to be $52$ percent of capacity; actual usage was $52$ percent of capacity. A smothing constant of $\mathrm{.}20$ is used. Problem $3-3($Algo$)$

A dry cleaner uses exponential smoothing to forecast equipment usage at

its main plant. August usage was forecasted to be $52$ percent of capacity;

actual usage was $52$ percent of capacity. A smoothing constant of $\mathrm{.}20$ is

used.

a$.$ Prepare a forecast for September.

Note: Round your final answer to $2$ decimal places.

Forecast for September

percent of capacity

b$.$ Assuming actual September usage of $59$ percent, prepare a forecast

for October usage.

Note: Round your answer to $2$ decimal places.