Home > APCALC > Chapter 11 > Lesson 11.4.1 > Problem11-115

11-115.

Multiple Choice: The luminous intensity $E$ of a light bulb, measured in lumens/ft2, varies inversely as the square of the distance $s$ from the bulb. $E = 5.2$ lumens/ft2 when $s = 5 \text{ ft}$ for a $100$ watt bulb. If you are moving away from a $100$ watt bulb at a speed of $2$ ft/sec and you are $3$ feet from the bulb, the luminous intensity is changing at the rate of:

1. $- \frac { 520 } { 27 }$ lumens/ft

1. $- \frac { 260 } { 27 }$ lumens/ft

1. $- \frac { 130 } { 27 }$ lumens/ft

1. $- \frac { 130 } { 9 }$ lumens/ft

1. $- \frac { 260 } { 9 }$ lumens/ft

$E=\frac{k}{s^2}$

$5.2=\frac{k}{5^2}\text{ }k=?$

When $s = 3, E =$ ?

$\frac{d}{dt}(Es^2)=\frac{d}{dt}(k)$

$E^\prime s^2+2Ess^\prime=0$

Substitute in the known values and solve for E′.