Subjects algebra

Exponential Growth 7787E6

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1. **State the problem:** We have 250 plants growing at a rate of 40% per month. We want to find the number of plants after 3 months. 2. **Formula used:** The exponential growth formula is $$\text{Future Amount} = I(1 + r)^t$$ where: - $I$ is the initial amount (250 plants), - $r$ is the growth rate (as a decimal), - $t$ is the time in months (3 months). 3. **Identify the growth rate:** 40% as a decimal is $0.40$. So, $r = 0.40$. 4. **Plug values into the formula:** $$\text{Future Amount} = 250(1 + 0.40)^3$$ 5. **Calculate inside the parentheses:** $$1 + 0.40 = 1.40$$ 6. **Raise to the power of 3:** $$1.40^3 = 1.40 \times 1.40 \times 1.40 = 2.744$$ 7. **Multiply by initial amount:** $$250 \times 2.744 = 686$$ 8. **Final answer:** After 3 months, there will be approximately **686 plants**. **The number that belongs in the green box is $0.40$.**