In July 2021, Vio Bank was offering 0.61% interest on its money market account.† Assuming interest is reinvested daily, find the associated exponential model for the value of a $2,000 deposit after t years. Hint: [See this example.]
A(t) = 
  
Incorrect: Your answer is incorrect.

To solve this, we'll use the exponential growth formula, which is typically expressed as:

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

Where:
- $ A(t) $ is the amount of money after $ t $ years,
- $ P $ is the initial principal (the initial deposit, which is $2,000 in this case),
- $ r $ is the annual interest rate (0.61% or 0.0061),
- $ n $ is the number of times the interest is compounded per year (since it's compounded daily, $ n = 365 $),
- $ t $ is the number of years.

### Step-by-step:
1. **Principal:** $ P = 2,000 $
2. **Annual interest rate:** $ r = 0.0061 $
3. **Daily compounding:** $ n = 365 $
4. **Exponential model equation:**

Substitute these values into the exponential growth formula:

\[
A(t) = 2000 \left(1 + \frac{0.0061}{365}\right)^{365t}
\]

This is the exponential model that represents the value of a $2,000 deposit after $ t $ years with a 0.61% annual interest rate compounded daily.

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Do you want further details or have any questions about this process?

### Related Questions:
1. How would the formula change if the interest were compounded monthly instead of daily?
2. What would be the value of the deposit after 5 years using this model?
3. How would the exponential model differ if the interest rate were 1.5% instead of 0.61%?
4. How does the frequency of compounding (daily, monthly, annually) affect the growth of the deposit?
5. Can this model be applied to interest rates that change over time?

### Tip:
The more frequently interest is compounded, the faster your money grows—this is because of the effect of "compound interest."

In July 2021, Vio Bank was offering 0.61% interest on its money market account. Assuming interest is reinvested daily, find the associated exponential model for the value of a $2,000 deposit after t years. Hint: [See this example.]

Discover how to calculate the exponential growth model for a $2,000 deposit with a 0.61% interest rate compounded daily. This example uses the formula A(t) = P(1 + r/n)^(nt) to explain compound interest and exponential growth. Ideal for high school students studying algebra and finance.

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