Find an Exponential Function of Theform $P(t) = y_{0} e^{k t}$

Multiple Choice

Find an exponential function of theform $P(t) = y_{0} e^{k t}$ to model the given data.
-In 1985, the number of female athletes participating in Summer Olympic-Type Games was 550. In 1996, about 3550 participated in the Summer Olympics in Atlanta. Assuming that $P(0) =500$ and that the exponential model applies, find the value of $\mathrm{k}$ rounded to the hundredths place, and write the function.

A) $\mathrm{k}=0.17 ; \mathrm{P}(\mathrm{t}) =500 \mathrm{e}^{0.17 \mathrm{t}}$
B) $\mathrm{k}=0.17 ; \mathrm{P}(\mathrm{t}) =500 \mathrm{e}^{0.27 \mathrm{t}}$
C) $\mathrm{k}=0.19 ; \mathrm{P}(\mathrm{t}) =500 \mathrm{e}^{0.19 \mathrm{t}}$
D) $k=0.16 ; \mathrm{P}(\mathrm{t}) =500 \mathrm{e}^{0.16 \mathrm{t}}$