A factory multiplies it's production by 1.5 from Saturday to Thursday everyday if the production difference between Monday and Wednesday is 4.5 tons how many tons are produced at Thursday 

Let's define the production on Saturday as \( P \) tons. Since the production multiplies by 1.5 every day from Saturday to Thursday, we can express the production on each day as follows:

- Saturday: \( P \) tons
- Sunday: \( 1.5P \) tons
- Monday: \( 1.5^2P = 2.25P \) tons
- Tuesday: \( 1.5^3P = 3.375P \) tons
- Wednesday: \( 1.5^4P = 5.0625P \) tons
- Thursday: \( 1.5^5P = 7.59375P \) tons

According to the problem, the difference in production between Monday and Wednesday is 4.5 tons. Therefore, we set up the following equation:

\[ 5.0625P - 2.25P = 4.5 \]

Simplifying this:

\[ 2.8125P = 4.5 \]

To find \( P \), we divide both sides of the equation by 2.8125:

\[ P = \frac{4.5}{2.8125} \]

\[ P = 1.6 \]

Now, we need to find the production on Thursday, which is \( 1.5^5P \):

\[ 1.5^5 \times 1.6 = 7.59375 \times 1.6 \]

\[ = 12.15 \]

Therefore, the production on Thursday is \( 12.15 \) tons.

Would you like any more details or have any questions?

Here are 8 related questions to consider:

1. What is the production on Tuesday?
2. How much is the production difference between Tuesday and Thursday?
3. What is the percentage increase in production from Monday to Wednesday?
4. How many days will it take to double the production from Saturday?
5. If the production continues to grow by 1.5 each day, what will it be on Friday?
6. What is the total production from Saturday to Thursday?
7. What would be the production if the multiplication factor was 2 instead of 1.5?
8. If production started at 2 tons on Saturday, what would it be on Thursday?

**Tip:** When dealing with exponential growth problems, identifying the base rate and applying it correctly over the desired period is crucial for accurate calculations.

Explore how a factory's production increases by 1.5 daily from Saturday to Thursday, with specific calculations showing a production of 12.15 tons on Thursday. Learn about exponential growth and arithmetic progression in this math problem suitable for Grades 10-12.

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