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Answer :
We are given the function
$$
f(t) = 3600(1.035)^t,
$$
which represents the amount of money in a savings account after $t$ years. Here’s a step-by-step explanation:
1. In an exponential function of the form
$$
f(t) = A(1+r)^t,
$$
the constant $A$ is the initial amount in the account. This is because when $t = 0$, we have
$$
f(0) = A(1+r)^0 = A \times 1 = A.
$$
2. Substituting $t = 0$ in the given function yields:
$$
f(0) = 3600(1.035)^0 = 3600 \times 1 = 3600.
$$
3. This calculation shows that the account starts with $\$3600$. It is not an amount that is added each year or a decrease, but rather the amount present at the very beginning.
4. Therefore, the value $3600$ represents the initial amount in the savings account.
Thus, the correct interpretation is:
$$\textbf{The initial amount in the account is } \$3600.$$
$$
f(t) = 3600(1.035)^t,
$$
which represents the amount of money in a savings account after $t$ years. Here’s a step-by-step explanation:
1. In an exponential function of the form
$$
f(t) = A(1+r)^t,
$$
the constant $A$ is the initial amount in the account. This is because when $t = 0$, we have
$$
f(0) = A(1+r)^0 = A \times 1 = A.
$$
2. Substituting $t = 0$ in the given function yields:
$$
f(0) = 3600(1.035)^0 = 3600 \times 1 = 3600.
$$
3. This calculation shows that the account starts with $\$3600$. It is not an amount that is added each year or a decrease, but rather the amount present at the very beginning.
4. Therefore, the value $3600$ represents the initial amount in the savings account.
Thus, the correct interpretation is:
$$\textbf{The initial amount in the account is } \$3600.$$
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Rewritten by : Jeany
