1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?A. 5.88 x 10^13 milesB. 5.76 x 10^14 milesC. 5.88 x 10^12 milesD. 9.8 x 10^12 miles2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?A. $4,979.11B. $14,920.54C. $112,992.00D. $15,494.70
Accepted Solution
A:
1. Distance: d=9.8x10^1 light years d=9.8x10^1x5.88x10^12 miles d=57.6x10^13 miles d=5.76x10^14 miles
Answer: Option B. 5.76x10^14 miles
2. Principal: P=1,600 Annual interest: i=7%=7/100→i=0.07 Number of years: t=33 Balance: B=? Compounded semiannually (twice per year) → n=2
B=P(1+i/n)^(nt)
Replacing the values: B=$1,600(1+0.07/2)^(2x33) B=$1,600(1+0.035)^66 B=$1,600(1.035)^66 B=$1,600(9.684185201) B=$15,494.69632 B=$15,494.70