Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of the function at that point.

\(f(x,y)=y+sin(x/y), (0,3)\)

Solve the exponential equation \(3^x=81\) by expressing each side as a power of the same base and then equating exponents.

Choose the correct letter. Which of the following functions models exponential decay?

A. \(f(x)=12*3^x\)

B. \(y=2*0.8^x\)

C. \(y=-3x^2\)

D. \(f(x)=1.8^x\)

Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data.

\(\begin{array}{|c|c|} \hline x&0&1&2&3&4\\ \hline y&10089&578&968&457&8\\ \hline \end{array}\)

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. \(5 ≤ 3 + |2x− 7|\)