Calculus - Logs/ Exponential Functions

Question

The function that grows at a rate equal to its value is:

1. exponential function with any base

2.logarithmic function with base e

3.logarithmic function with any base

4.exponential function with base e

Answer 1

The function satisfies dy/dx = ky where k is a constant

dy/y = k dx

integrating

ln |y| = kx + C

|y| = e^{kx + C} = e^kx e ^C

= A e^kx where A, and k are constants

so (4)