def fit(k):
loss = 0.0
for total_n, deltas in all_deltas:
total_k = total_n
P = 1.0
for t in sorted(deltas.keys()):
delta_k, delta_n = deltas[t]
pred = total_n * math.exp(-k * t / YEAR)
loss += (total_n * P - pred)**2
P *= 1 + delta_k / total_n
total_k += delta_k
total_n += delta_n
print(k, loss)
return loss
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