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Sagot :
Step 1. The information we have is.
The initial amount of the investment which is called the principal P is:
[tex]P=3500[/tex]The interest rate is 7.05%, this will be r:
[tex]r=7.05\text{ percent}[/tex]We will need to represent the interest rate as a decimal number, for that, we divide by 100:
[tex]\begin{gathered} r=\frac{7.05}{100} \\ \downarrow \\ r=0.0705 \end{gathered}[/tex]As additional variables, we will have:
[tex]\begin{gathered} A\longrightarrow\text{Total amount} \\ t\longrightarrow\text{time of the investment} \end{gathered}[/tex]Step 2. Use the Continuous compounding formula:
[tex]A=Pe^{rt}[/tex]where A is the amount including interest, P is the principal amount of the investment, r is the interest rate, and t in years.
Also, e is a constant which is equal to:
[tex]e\approx2.783[/tex]But we will only represent it as e.
Step 3. Substitute P and r into the continuous compounding formula:
[tex]\boxed{A=3500e^{0.0705\times t}}[/tex]That is the equation that models the situation.
Answer:
[tex]\boxed{A=3500e^{0.0705\times t}}[/tex]
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