Find an exponential function of the form \( \mathrm{P}(\mathrm{t})=\mathrm{y}_{0} e^{\mathrm{kt}} \) to model the given data. In 1985 , the number of female athletes participating in Summer Olympic-Type Games was 550. In 1996, about 3,650 participated in the Summer Olympics-Type games. Assuming that \( P(0)=550 \) and that the exponential model applies, find the value of k rounded to the hundredths place, and write the function. A. \( \mathrm{k}=0.16 ; \mathrm{P}(\mathrm{t})=550 e^{0.16 t} \) B. \( \mathrm{k}=0.17 ; \mathrm{P}(\mathrm{t})=550 e^{0.17 t} \) C. \( \mathrm{k}=0.27 ; \mathrm{P}(\mathrm{t})=550 e^{0.27 t} \) D. \( \mathrm{k}=0.19 ; \mathrm{P}(\mathrm{t})=550 e^{0.19 t} \)

257. Funksiýalaryň grafigini guruń: \( \begin{array}{ll}\text { a) } y=x^{2}+6 x ; & \text { c) } y=0,5 x^{2}-4 \\ \text { b) } y=-\frac{1}{2} x^{2}+2 ; & \text { d) } y=\frac{1}{2} x^{2}-3 x\end{array} \)

Determine la forma polar del complejo \( z=-3-\sqrt{3} i \)

Find \( \|\mathbf{v}\| \). \( \begin{array}{l}\mathbf{v}=9 \mathbf{i}-12 \mathbf{j} \\ \|\mathbf{v}\|=\square \text { (Type an exact answer, using radicals as needed. Simplify your answer.) }\end{array} \)

Write the vector v in the form \( \mathrm{ai}+\mathrm{bj} \), given its magnitude \( \|\mathrm{v}\| \) and the angle \( \alpha \) it makes with the positive \( x \)-axis, \[ \alpha v=45^{\circ} \] \( \mathrm{v}=\square \) (Simplify your answer. Type an exact answer using radicals as needed. Type your answer in the form ai + bj.)

Suppose that the functions \( f \) and \( g \) are defined as follows. \[ \begin{array}{l}f(x)=2 x+3 \\ g(x)=\sqrt{4 x+1} \\ \text { Find } \frac{f}{g} \text { and } f-g \text {. Then, give their domains using interval notation. } \\ \begin{array}{l}\left(\frac{f}{g}\right)(x)=\square \\ \text { Domain of } \frac{f}{g}: \square \\ \text { Domain of } f-g: \square\end{array} \\ \qquad\end{array} \] \( \begin{array}{l}\qquad-g)=\square\end{array} \) \[ \]