sara is on a diet. she currently weighs 82.5kg and intends to lose 0.5% of her weight every day. will she meet her target of 70kg within 25 days

To determine whether Sara will meet her target of 70 kg within 25 days by losing 0.5% of her weight each day, we can use the following steps:

### Step 1: Understand the daily weight loss
Sara loses 0.5% of her weight each day. This can be expressed as:
\[
\text{New weight after one day} = \text{Current weight} \times (1 - 0.005)
\]
This means each day, her weight is multiplied by 0.995.

### Step 2: Calculate her weight after 25 days
We can use the formula for exponential decay to find her weight after 25 days:
\[
\text{Weight after 25 days} = 82.5 \times (0.995)^{25}
\]

### Step 3: Calculate the result
Let's compute the weight after 25 days.

\[
\text{Weight after 25 days} = 82.5 \times (0.995)^{25}
\]

\[
\text{Weight after 25 days} \approx 82.5 \times 0.88285 \approx 72.82 \text{ kg}
\]

### Conclusion:
After 25 days, Sara's weight will be approximately **72.82 kg**. Since her target is 70 kg, she **will not meet her target** of 70 kg within 25 days.

Would you like a detailed explanation or have any questions?

Here are some related questions:
1. How many days would it take for Sara to reach exactly 70 kg?
2. What would her weight be after 30 days of losing 0.5% per day?
3. How would the outcome change if she lost 1% of her weight per day?
4. What is the percentage loss after 25 days from her original weight?
5. Can this method of weight loss be considered a linear or exponential process?

**Tip:** Exponential decay is a common model for processes where a percentage is lost repeatedly, such as in weight loss, depreciation, or radioactive decay.

Explore Sara's weight loss journey over 25 days with mathematical precision. Calculate her daily weight loss percentage and determine if she'll reach her target weight of 70 kg. Get detailed step-by-step solutions and answers to related questions. Perfect for advanced high school students and math enthusiasts.

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