3. An essential oil has antimicrobial activity with an MIC of 15 mg/Kg and can be used as a bio preservative.
This activity is lost at the rate of 1% of the remaining concentration, per day. The minimum amount of oil to
be added (mg) to 1 Kg of food product that is stored for 30 days is:
1. 21.43
2. 17.65
3. 20.28
4. 19.50

How to Calculate the Minimum Dose of a Natural Preservative with Degradation Over Time

When using natural preservatives like essential oils in food, one must account for their degradation over time to ensure effectiveness. The Minimum Inhibitory Concentration (MIC) must be maintained over the entire storage period for the antimicrobial effect to persist.

Let’s solve a practical problem using this concept:

Question:

An essential oil has antimicrobial activity with an MIC of 15 mg/kg and can be used as a bio-preservative. This activity degrades at a rate of 1% of the remaining concentration per day.
What is the minimum amount of essential oil (in mg) that must be added to 1 kg of food to retain the MIC after 30 days?

Options:

1. 21.43

2. 17.65

3. 20.28

4. 19.50

Step-by-Step Explanation:

This is a classic exponential decay problem where a substance degrades at a fixed percentage of its remaining amount per unit time.

1. Formula for exponential decay:

Ct=C0⋅(1−r)tC_t = C_0 \cdot (1 – r)^tCt​=C0​⋅(1−r)t

Where:

• CtC_tCt​: concentration after time $t$

• C0C_0C0​: initial concentration

• $r$: daily decay rate (1% = 0.01)

• $t$: time in days (30 days)

We are given:

• Ct=15C_t = 15Ct​=15 mg (MIC to be maintained at day 30)

• $r=0.01$

• $t=30$

We need to solve for C0C_0C0​ — the initial concentration required:

15=C0⋅(0.99)3015 = C_0 \cdot (0.99)^{30}15=C0​⋅(0.99)30

Calculate (0.99)30(0.99)^{30}(0.99)30:

(0.99)30≈0.7397(0.99)^{30} \approx 0.7397(0.99)30≈0.7397

Now solve for C0C_0C0​:

C0=150.7397≈20.28 mgC_0 = \frac{15}{0.7397} \approx 20.28\ \text{mg}C0​=0.739715​≈20.28 mg

✅ Correct Answer: (3) 20.28 mg

Why This Matters

Natural preservatives like essential oils are gaining popularity in clean-label food products. However, their efficacy can degrade over time due to environmental factors like:

• Temperature

• Light

• Oxidation

This means calculating the right dose to maintain antimicrobial activity for the full shelf life is critical.

Summary

To ensure that the MIC of 15 mg/kg is still present after 30 days of 1% daily degradation:

• Use exponential decay formula

• Calculate backward to find the initial required concentration

• Final answer: 20.28 mg per 1 kg of food