The paper considers the problem of continuous-time online frequency estimation for a sinusoidal signal with a time-varying amplitude, where the latter is given by a known function of time multiplied by an unknown constant. To solve the problem a novel parameterization method is applied yielding linear regression with three unknown constant parameters. Next, two estimation algorithms are proposed, where the first is based on the conventional gradient approach, and a recently presented dynamic regressor extension and mixing procedure is used for the second. Global exponential convergence of the suggested frequency estimator is established, and the obtained performance is illustrated with simulations.