A sample of radiative substance is found `90%` of it’s initial amount after one day. What `%` of the original sample can be found after 3 days ?

Options

A. 81
B. 72.9
C. 25
D. `65.61`

Explanation

To solve the problem step by step, we need to understand the concept of radioactive decay and how it applies to the given situation.

### Step 1: Understand the initial conditions
We start with an initial amount of a radioactive substance, which we can denote as 100%. After one day, it is given that 90% of the initial amount remains.

**Hint:** Remember that the remaining percentage after decay is crucial for calculating future amounts.

### Step 2: Determine the fraction remaining after one day
After one day, the fraction of the substance remaining is:
\[ \text{Fraction remaining after 1 day} = \frac{90}{100} = 0.90 \]

**Hint:** Convert percentages to fractions to simplify calculations.

### Step 3: Apply the concept of equal fraction decay
Since the decay is first-order, the same fraction of the substance will decay in equal time intervals. Therefore, if we want to find the remaining amount after 3 days, we can raise the fraction remaining after one day to the power of the number of days.

**Hint:** Use the formula \( \text{Remaining fraction} = (\text{Fraction after 1 day})^{\text{number of days}} \).

### Step 4: Calculate the remaining fraction after 3 days
Using the fraction from Step 2:
\[ \text{Remaining fraction after 3 days} = (0.90)^3 \]
Calculating this gives:
\[ (0.90)^3 = 0.729 \]

**Hint:** Make sure to perform the exponentiation carefully.

### Step 5: Convert the remaining fraction to percentage
To find the percentage of the original sample remaining after 3 days, we multiply the remaining fraction by 100:
\[ \text{Percentage remaining after 3 days} = 0.729 \times 100 = 72.9\% \]

**Hint:** Always convert decimal fractions back to percentages for the final answer.

### Conclusion
After 3 days, the percentage of the original sample that can be found is **72.9%**.

**Final Answer:** 72.9%