Exponential function with espected behavior - removal experiment in ecology

I'm working with bird fatalities in windfarms and one of the required parameters to estimate mortality is the probability of an animal remain in the field at a given time, in order to be available for detection while a field work session. (which will be another probability to be accounted for).

Typically bird carcass removal by animals will follow a negative exponential curve. It's very probable that a bird will be removed by a carnivore in the first few days after fatality. There are well described equations to evaluate mortality using there parameters.

What I'm trying to achieve is a exponential function with two particular behaviors. 1 - be limited by one at day zero.and tend to zero.

Any help will be appreciated