NAME: ______________________________________________
INVESTIGATION R – 1 VARIATIONS
1. Under certain conditions of artificial light, the exposure time required to photograph an
object varies directly as the candlepower of the light and varies inversely as the square of
the object’s distance from the light source. The exposure time is 0.01 seconds when the
light source is 6.00 feet from the object.
A. Determine the constant of variation: k = __________
B. Provide the equation for exposure time: ___________________________________
C. How far from the object should the light source be when both the candlepower and
the exposure time are doubled?
2. Heat loss, h, in calories per hour through a glass window varies jointly as the difference,
d, between the inside and outside temperatures and as the area, A, of the window and
inversely as the thickness, t, of the pane of glass. If the temperature difference is 30F,
there is a heat loss of 9000 calories per hour through a window with an area of 1500
cubic centimeters and thickness of 0.25 centimeters.
A. Determine the constant of variation: k = __________
B. Provide the equation for heat loss: ___________________________________
C. Find the heat loss through a window with the same area and a thickness of 0.2
centimeter when the temperature difference is 15F.
3. There are many forces that work together to make both airplanes and birds fly.
Although wing shape varies greatly among birds, the number of wing beats per second
for any bird in flight is approximately inversely related to the length of its wing.
A. Find the approximate constant of variation, k, to the nearest tenth, if a herring gull
flaps its wings at a rate of about 2.8 wing beats per second and has a wing length of
about 24.1 centimeters.
B. Use the approximate value of k from A to find the approximate number of wing
beats per second for a starling that has a wing length of about 13.2 centimeters.
C. Use the approximate value of k from part A to find the approximate wing length of a
cormorant who flaps its wings at a rate of about 1.9 wing beats per second.