There is a constant growth rate (in %) every year in the production of a company as seen in the given table.

| Year | 2018 | 2019 | 2020 |
|-------|-------|-------|-------|
| Production (in units) | 9000 | 10800 | X |

Find the value of *X* from the data given in the table.

Question

There is a constant growth rate (in %) every year in the production of a company as seen in the given table.

| Year | 2018 | 2019 | 2020 |
|-------|-------|-------|-------|
| Production (in units) | 9000 | 10800 | X |

Find the value of *X* from the data given in the table.

Accepted Answer

**Solution:**

1. Let the constant growth rate be *r*% per year.

2. Production in 2018 = 9000 units

3. Production in 2019 = 10800 units

4. Using the growth formula:
   $$	ext{Production in 2019} = 	ext{Production in 2018} 	imes \left(1 + \frac{r}{100}ight)$$

Substitute the values:
   $$10800 = 9000 	imes \left(1 + \frac{r}{100}ight)$$

5. Solve for *r*:
   $$1 + \frac{r}{100} = \frac{10800}{9000} = 1.2$$

$$\frac{r}{100} = 0.2 \implies r = 20\%$$

6. Now, find production in 2020:
   $$X = 10800 	imes \left(1 + \frac{20}{100}ight) = 10800 	imes 1.2 = 12960$$

**Answer:** $12960$

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