Question

the function ( f ), defined by ( f(t) = 1,000 cdot (1.07)^t ), represents the amount of money in a bank account ( t ) years after it was opened.

a. how much money was in the account when it was opened?

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Explanation:

Step1: Identify the time when opened

When the account was opened, \( t = 0 \) (since \( t \) is years after opening).

Step2: Substitute \( t = 0 \) into \( f(t) \)

The function is \( f(t)=1000\cdot(1.07)^t \). Substitute \( t = 0 \):
\( f(0)=1000\cdot(1.07)^0 \).
Since any non - zero number to the power of 0 is 1, \( (1.07)^0 = 1 \).
So \( f(0)=1000\times1 = 1000 \).

Answer:

\( \$1000 \)