SAT Mathematics Practice Test 2

If IA is the intensity measured by Observer A from a distance of rA and IB is the intensity measured by Observer B from a distance of rB,then IA=16IB Using the formula I=

P

4π2

,he intensity measured by Observer A is IA=

P

4πrA2

,which can also be written in terms of IB as IA=16IB=16(

P

4πrB2

).Setting the right-hand sides of these two equations equal to each other gives

P

4πrA2

=16(

P

4πrB2

) which relates the distance of Observer A from the radio antenna to the distance ofObserver B from the radio antenna. Canceling the common factor

p

4π

and rearranging the equation gives rB2=16rA2 Taking the square root of each side of rB2=16rA2 gives rB=4rA and then dividing each side by 4 yields rA=

1

4

rB.Therefore, the distance of Observer A from the radio antenna is

1

4

the distance of Observer B from the radio antenna.
Choices B, C, and D are incorrect and may result from errors in deriving or using the formula

P

4πrA2

=(16)(

P

4πrB2

)