For an **exponential growth trend**, the increase from £190 to £3,367 over 12 months follows a curve where growth accelerates each month. To model this, we need to calculate the constant monthly growth rate using the formula for exponential growth:

\[
V(t) = V_0 \times (1 + r)^t
\]

Where:
- \( V(t) \) is the final value after time \( t \),
- \( V_0 \) is the initial value,
- \( r \) is the monthly growth rate,
- \( t \) is the number of months.

Given that:
- \( V_0 = 190 \),
- \( V(12) = 3367 \),
- \( t = 12 \),

We can solve for the growth rate \( r \).

### Solving for the growth rate:
\[
3367 = 190 \times (1 + r)^{12}
\]
\[
(1 + r)^{12} = \frac{3367}{190} = 17.72
\]
\[
1 + r = \sqrt[12]{17.72}
\]
\[
1 + r \approx 1.392
\]
\[
r \approx 0.392 \text{ or } 39.2\%
\]

Thus, the monthly growth rate is approximately **39.2%**. Using this rate, the values for each month can be calculated by applying the formula.

Let's calculate the monthly values.

### Exponential Growth Trend

| Month   | Value (£) |
|---------|-----------|
| Month 1 | 190       |
| Month 2 | 264.48    |
| Month 3 | 368.12    |
| Month 4 | 512.42    |
| Month 5 | 713.24    |
| Month 6 | 993.10    |
| Month 7 | 1,383.11  |
| Month 8 | 1,926.90  |
| Month 9 | 2,685.71  |
| Month 10| 3,745.52  |
| Month 11| 5,223.83  |
| Month 12| 3,367     |

This table shows how the value grows exponentially each month, with increasing increments as time progresses.

Would you like a graph of this trend?

#### Follow-up Questions:
1. Do you need any adjustments to the monthly growth rate?
2. Would you like a graph comparing the exponential and linear growth trends?
3. Should I explain further how the monthly values are calculated?
4. Do you need help applying this model to a real-life scenario?
5. Would you like to explore other growth models, such as logarithmic or polynomial growth?

**Tip:** Exponential growth models are useful when projecting rapid increases, like in investments or populations, but can quickly become

For an exponential growth trend, how can I model the increase from £190 to £3,367 over 12 months and calculate the monthly growth rate?

Learn how to calculate the monthly growth rate for an exponential increase from £190 to £3,367 over 12 months. This problem covers key algebraic concepts, including the exponential growth formula and applying it to real-life scenarios. Suitable for students in Grades 10-12.

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