 The current price of a certain property is 2,500,000 and is increasing at the rate of 5% every year. After how many years will the price increase by 60% of the current price?


using the growth function 

To solve this problem using the growth function, we use the formula for exponential growth:

\[
P(t) = P_0 \cdot e^{rt}
\]

where:
- \( P(t) \) is the price after time \( t \),
- \( P_0 \) is the initial price,
- \( r \) is the growth rate (in decimal form),
- \( t \) is the time in years.

In this case:
- Initial price \( P_0 = 2,500,000 \)
- Growth rate \( r = 5\% = 0.05 \)
- We want to find \( t \) such that the price increases by 60% of the current price. This means the final price \( P(t) = 2,500,000 + 0.60 \times 2,500,000 = 4,000,000 \).

Plugging in the values, we have:

\[
4,000,000 = 2,500,000 \cdot e^{0.05t}
\]

Now, let's solve for \( t \).It will take approximately 9.4 years for the price of the property to increase by 60% of its current value.

Do you want more details or have any other questions?

Here are 5 related questions to explore further:

1. What will be the property price after 10 years if the growth rate remains constant?
2. How much will the property value increase after 15 years at the same growth rate?
3. What if the growth rate changes to 7% per year? How long will it take to reach a 60% increase then?
4. How does the exponential growth function compare to a simple linear growth model?
5. What would be the required growth rate to reach a 60% increase in exactly 8 years?

**Tip:** Understanding exponential growth is crucial in finance and economics, as it accurately models situations where growth compounds over time, such as investments or property values.

The current price of a certain property is 2,500,000 and is increasing at the rate of 5% every year. After how many years will the price increase by 60% of the current price?

Solve the exponential growth problem where the current price of a property is 2,500,000 and it grows by 5% annually. Find out how many years it will take for the price to increase by 60% of its current value. Includes key formulas and step-by-step calculations.

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