If I have 30$ that grows 7% every ten minutes how long would it take to reach $2800

To find out how long it would take for $30 to grow to $2800 with a 7% growth every ten minutes, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- $ A $ is the final amount ($2800),
- $ P $ is the initial amount ($30),
- $ r $ is the growth rate per period (7% or 0.07),
- $ n $ is the number of compounding periods per unit of time (in this case, since the growth happens every 10 minutes, $ n = 1 $),
- $ t $ is the time in minutes divided by 10 (since the growth occurs every 10 minutes).

We need to solve for $ t $.

Let's solve this equation:

\[
2800 = 30 \left(1 + 0.07\right)^t
\]

First, we simplify:

\[
\frac{2800}{30} = (1.07)^t
\]

\[
\frac{2800}{30} = 93.33 \approx (1.07)^t
\]

Next, take the logarithm of both sides to solve for $ t $:

\[
\log(93.33) = t \log(1.07)
\]

Finally, solve for $ t $:

\[
t = \frac{\log(93.33)}{\log(1.07)}
\]

I'll calculate this next.It would take approximately 67 ten-minute periods for your $30 to grow to $2800 at a 7% growth rate every ten minutes. 

This translates to about **670 minutes** (or approximately **11 hours and 10 minutes**).

Would you like further details or have any other questions?

Here are 5 related questions you might find interesting:
1. What if the growth rate was 10% instead of 7%?
2. How long would it take to reach $2800 if the initial amount was $50?
3. What if the compounding period was every 5 minutes instead of every 10 minutes?
4. How much would $30 grow in 24 hours with the same 7% growth every 10 minutes?
5. How can compound interest be applied to real-world financial planning?

**Tip:** When dealing with exponential growth, the time it takes to reach a goal can be significantly reduced with even small increases in the growth rate!

Discover how long it would take for $30 to grow to $2800 with a 7% growth rate every ten minutes using compound interest formulas and logarithms. Learn the step-by-step calculation and its real-world implications.

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