Question 1035565: Based on data from June 2006, the forecast for maximum 5-day snow runoff volumes for the American River at Folsom, CA, can be modeled by
v = f(t) = −2.606t + 131.8
thousand acre-feet, where t is the number of days since the end of May 2006.That is, the model forecasts the snow runoff for the 5-day period beginning on the selected day of June 2006. Find the inverse function.
f −1(v) =
Determine the value of f^ −1(61.7).
(Round your answer to two decimal places.)
f^ −1(61.7) =
Interpret the real-world meaning of the result.
The snow runoff volume is acre-feet days after the end of May, 2006.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation is y = f(t) = 2.606*t + 131.8
to find the inverse equation, replace y with t and replace t with y to get:
t = -2.606*y + 131.8
solve for y to get y = (t - 131.8) / -2.606
your normal equation is y = -2.606 * t + 131.8
your inverse equation is y = (t - 131.8) / -2.606
if you allow t to be equal to 61.7 in the inverse equation, you will get y = 26.89946278.
if you allow t to be equal to 26.89946278 in the normal equation, you will get y = 61.7.
the normal equation tells you that, if you are 26.89946278 days after the end of may 2006, then the maximum expected 5 day runoff volume is 61.7 thousand acre feet.
the inverse equation tells you that, if you expect the maximum 5 day runoff volume to be 61.7 thousand acre feet, then that would occur 26.89946278 days after the end of may 2006.
in the normal equation, y represents the number of thousand acre feet and t represents the number of days.
in the inverse equation, y represents the number of days and t represents the number of thousand acre feet.
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