To model the number of fish in the lake using an exponential decay function, we can start with the general formula for exponential decay:
where:
is the quantity at time , is the initial quantity, is the decay constant, is the time in years, is the base of the natural logarithm.
In this case, we have:
(the initial number of fish),- the decay rate is 3%, which can be represented as a decay constant of
.
Thus, the exponential decay function for the number of fish in the lake can be modeled as:
Next, we need to find the number of fish in the lake in 2025. Since 2015 is our starting point, we compute
Now we substitute
Calculating
So we have:
Now we need to compute
Now we can plug this value back into the function:
Rounding to the nearest whole fish, we find:
Thus, the estimated number of fish in the lake in 2025 is approximately 1482 fish.