The winning time int he womens Olympic 200 meter dash w is a function of the year x in which the event was run, starting with 1948 and is given by the equation
w= f(X)= -0.0661X+152.8
A. PREDICT THE WINNING TIME FOR THE 1988 OLYMPICS. ( THE ACTUAL TIME WAS 21.34 SECONDS)
B. FIND F^-1(W)
C. USE F^-1(W) TO PREDICT IN APPROXIMATELY WHAT YEAR THE WINNING TIME WILL BE 20 SECONDS
To find the answers to these questions, you need to understand the given equation and how it relates to the question being asked.
The equation given is:
w = f(x) = -0.0661x + 152.8
A. To predict the winning time for the 1988 Olympics, we need to substitute the year x with 1988 in the equation and solve for w.
w = -0.0661 * 1988 + 152.8
w = -130.9568 + 152.8
w = 21.8432
So, the predicted winning time for the 1988 Olympics is approximately 21.84 seconds.
B. To find f^(-1)(w), we need to swap the variables x and w in the equation and solve for x.
x = (-w + 152.8) / -0.0661
When we substitute w with 21.34 (actual time in seconds for the 1988 Olympics), we get:
x = (-(21.34) + 152.8) / -0.0661
x = -1319.3
So, f^(-1)(w) is approximately -1319.3.
C. To predict in approximately what year the winning time will be 20 seconds, we need to substitute w with 20 in the equation f^(-1)(w).
x = (-(20) + 152.8) / -0.0661
x = -1238.93
Therefore, using f^(-1)(w), we can predict that the winning time of 20 seconds will occur approximately in the year -1238.93.
It's important to note that negative year values might not make sense in real-world scenarios, so in some cases, you may need to interpret the results accordingly.