Use a combined cost index and the power$-$sizing cost estimating model to estimate the current cost of a piece of equipment that has $50\%$ more capacity than a similar piece of equipment that cost $$30,000$ five years ago. The appropriate power$-$sizing exponent for this type of equipment is $0\mathrm{.}8,$ and the ratio of the cost indexes $($current to $5$ years ago$)$ is $1\mathrm{.}24.$

a$.$ $$55,800$

b$.$ $$29,760$

c$.$ $$44,640$

d$.$ $$51,454$