A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1088

The substance's half-life is 6.4 days

Step-by-step explanation:

Recall that the half life of a substance is given by the time it takes for the substance to reduce to half of its initial amount. So in this case, where they give you the constant k (0.1088) in the exponential form:

we can replace k by its value, and solve for the time "t" needed for the initial amount to reduce to half of its value (). Since the unknown resides in the exponent, to solve the equation we need to apply the natural logarithm:

which rounded to the nearest tenth is: 6.4 days

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