It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a × 10" where a is single digit. (1 point)

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Answer 1

To express the amount $15,528.23 in the form of \( a \times 10^n \) where \( a \) is a single digit, we follow these steps:

1. Identify the number in scientific notation:

   • The number $15,528.23 can be expressed as \( 1.552823 \times 10^4 \).

2. Round \( a \) to the nearest whole number:

   • Since we're looking to express it with a single digit, we round \( 1.552823 \) to \( 2 \) (the digit before the decimal point).

3. Determine \( n \):

   • From the scientific notation, \( n \) is \( 4 \).

Thus, we can express $15,528.23 as \( 2 \times 10^4 \).

Final Answer:

The amount \( 15,528.23 \) in the form of \( a \times 10^n \) is \( 2 \times 10^4 \).