Can anyone with this really struggling and trying to figure it out

9.6 days

Step-by-step explanation:

You want to find t such that y = (1/2)·y₀. That is, you want to solve

... (1/2)y₀ = y₀·e^(-0.072t)

Dividing by y₀, you have

... 1/2 = e^(-0.072t)

and taking the natural log gives ..

... ln(0.5) = -0.072t

... ln(0.5)/-0.072 = t ≈ 9.627 . . . . divide by the coefficient of t

The half-life is approximately 9.6 days.