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 x 10^n where "a" is single digit. (1 point)

Answer 1

To express the amount $15,528.23 in the form of \( a \times 10^n \), we first need to convert it into this scientific notation format, where \( a \) is a single digit.

1. Determine the value of \( a \) and \( n \):

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

2. Round \( a \):

   • We can round \( 1.552823 \) to one decimal place, which gives us \( 1.6 \).

3. Determine \( n \):

   • The exponent \( n \) is \( 4 \) because the decimal point was moved 4 places to the left to convert to scientific notation.

Therefore, the final result is:

\[ 1.6 \times 10^4 \]

So, the amount \( 15,528.23 \) expressed in the form of \( a \times 10^n \) is \( 1.6 \times 10^4 \).