To write an equation that models the growth of Michelle's investment, we can use the formula for compound interest, which is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested for.
For Michelle's investment:
- \( P = 1000 \)
- \( r = 0.03 \) (3% as a decimal)
- \( n = 4 \) (since the interest is compounded quarterly)
Substituting these values into the formula, we get:
\[ A = 1000 \left(1 + \frac{0.03}{4}\right)^{4t} \]
Now, simplifying the expression inside the parenthesis:
\[ \frac{0.03}{4} = 0.0075 \]
So the equation becomes:
\[ A = 1000 \left(1 + 0.0075\right)^{4t} \]
Which simplifies to:
\[ A = 1000 \left(1.0075\right)^{4t} \]
This is the equation that models the growth of Michelle's investment over time. If you have specific choices (responses a, b, c, d) to choose from, please provide them, and I can help identify the correct one.