Respuesta :
After 4 days the chlorine level reaches 1 ppm.
Explanation:
The formula N(t) = N₀ e⁽⁻kt⁾ models this decay process well, where
t = time measured in 24-hour days, so t =0, 1, 2, 3, ...
N₀ = initial measurement of HOCl at time t=0, just after first shocking the pool (given as 2.3 ppm)
N(t) = measurement of HOCl at time any time t (N at t=1 is given as 1.9 ppm)
e = exponential function
k = rate of decay constant
First, we have to find k from the measurements at t= 0 and t=1
N(1) = N(0) e⁽⁻k(1)) so 1.9 = 2.3 e⁻k and e⁻k = 1.9/2.3 = 0.826
Taking the logarithm of both sides: -k = ln (0.826) = - 0.191
so k = + 0.191
After 4 days,
N(4) = 2.3e⁻(0.191ₓ4) = 1.07 ≈ 1 ppm
After 4 days Geoff must shock the pool again.
