Question

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 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles


2. 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. $4,979.11
B. $14,920.54
C. $112,992.00
D. $15,494.70

Answer 1

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

Answer: Option D. $15,494.70