Question

A function whose derivative is a constant multiple of itself must be?

A) periodic
B) linear
C) exponential
D) quadratic
E) logarithmic

Answer 1

\[\large \begin{array}{rcl}
y'&=&ky \\
\frac{y'}{y}&=& k \\
\int \frac{y'}{y} dx &=& \int k dx \\
\ln(y) +C_1 &=& kx+C_2 \\
ye^{C_1} &=& e^{kx}e^{C_2} \\
y &=& Ce^{kx}
\end{array}\]What sort of function does this look like to you?

Answer 2

Keep in mind the independent variable is \(x\).

Answer 3

logarithmic?