Question 127641
It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 36000 km^2 in 40 days. Assuming that the area covered by the radioactive substance is a linear function of (t) time and is always circular in shape, express the radius (r) of the contamination as a function of (t). 
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Take the area of a circle equation; A = pi*r^2
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we want to solve for r
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pi*r^2 = A
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r^2 = {{{A/pi}}}
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r = {{{sqrt(A/pi)}}}
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Find the radius (km) after 40 days using the given area of 36000
r = {{{sqrt(36000/pi)}}}}
r = {{{sqrt(11459)}}}
r = 107 km
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Find the slope using the coordinates of 0,0 (0 days, 0 radius) and 40, 107
m = {{{107/40}}}
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r = {{{107/40}}}t; is the equation. (t (days) is on the x axis and the radius(km) is on the y axis):
if you graphed it would look like this:
{{{ graph( 300, 200, -20, 60, -50, 200, (107/40)x ) }}}
Using your calibrated eyeball, you can see on the graph that after 40 days the radius is about 100 km
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Did this make sense? Did it help you?