We study Escherichia coli chemotaxis behavior in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillates in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes smaller and out of phase with the attractant waveform. These observations are inconsistent with the well-known Keller-Segel chemotaxis equation. A new continuum model is proposed to describe the population level behavior of E. coli chemotaxis based on the underlying pathway dynamics. With the inclusion of a finite adaptation time and an attractant consumption rate, our model successfully explains the microfluidic experiments at different stimulus frequencies.