$1)$ Darren knows the information in the following table about assembly times of chair at his Furniture manufacturing. He notices that as more chairs are assembled the processing time per chair decreases.

a$)$ Fit a linear curve to the data. Insert equation and R$-$squared.

b$)$ Fit a power curve to the data. Insert equation and R$-$squared.

c$)$ Fit an exponential curve to the data. Insert equation and R$-$squared.

d$)$ Fit a logarithmic curve to the data. Insert equation and R$-$squared.

e$)$ Which curve fits best based on R$-$squared? Explain the interpretation of R$-$squared value.

f$)$ Use your answer from $($e$)$ to predict the $50$th unit's assembly time.