Coordinate with authorities regarding the production rate of the natural sources of income in your areas such as rice, coconut, or fish production Construct an exponential function corresponding to the production rate that you will be given

Every Monday to Thursday that person earn 500 each day but every Saturday to friday he earns 350 on each day and it increases into 5%

To construct an exponential function that represents the production rate (or earnings) based on the details provided, we can break down the problem into different parts. Here's the interpretation:

### Weekly Earnings Breakdown
1. **Monday to Thursday:** Each day, the person earns $ 500 $ units of currency.
   - Earnings for 4 days = $ 500 \times 4 = 2000 $ units.
   
2. **Saturday and Friday:** Each of these days, the person earns $ 350 $ initially. But every subsequent week, the earnings for Saturday and Friday increase by **5%**.

### Exponential Function for Friday and Saturday:
The earnings on Friday and Saturday follow an exponential growth model. If we let $ n $ represent the week number (starting from week 1), the earnings on Friday and Saturday can be modeled by the following formula:

\[
E(n) = 350 \times (1.05)^n
\]

Where:
- $ 350 $ is the initial amount earned on Friday and Saturday.
- $ 1.05 $ represents the 5% weekly increase.
- $ n $ is the week number.

### Total Weekly Earnings
To get the total weekly earnings, we sum the earnings for Monday to Thursday (which remain constant) and the earnings for Friday and Saturday (which grow exponentially). 

Let $ E_T(n) $ represent the total weekly earnings in week $ n $:

\[
E_T(n) = 2000 + 2 \times 350 \times (1.05)^n
\]

Where:
- $ 2000 $ is the constant earnings from Monday to Thursday.
- $ 350 \times (1.05)^n $ is the exponential growth for Friday and Saturday.
- The $ 2 \times $ factor accounts for both Friday and Saturday earnings.

### Exponential Function
Thus, the total earnings for each week, $ E_T(n) $, is given by the formula:

\[
E_T(n) = 2000 + 700 \times (1.05)^n
\]

This function represents the total weekly income where the Friday and Saturday earnings increase by 5% each week.

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Would you like further details on how to apply this exponential function to specific week numbers, or any other clarification?

### 5 Related Questions:
1. How do you calculate exponential growth in different contexts such as population or interest?
2. How would the earnings model change if the percentage increase was different?
3. What is the total amount earned after 10 weeks?
4. How can you model income for a different period, such as monthly or yearly, using this function?
5. Can you compare linear vs. exponential growth for similar income models?

### Tip:
Exponential growth can have a significant impact over time, even with small percentage increases, so it's important to track and understand its long-term effects.

Coordinate with authorities regarding the production rate of the natural sources of income in your areas such as rice, coconut, or fish production. Construct an exponential function corresponding to the production rate that you will be given. Every Monday to Thursday that person earns 500 each day but every Saturday to Friday he earns 350 on each day and it increases into 5%.

Learn how to construct an exponential function to model weekly earnings where a person earns $500 from Monday to Thursday and $350 on Friday and Saturday, increasing by 5% each week. Suitable for students in Grades 9-12.

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