in 1920 the record for a certain race was 45.7 seconds. In 1930, it was 45.4 seconds. Let R(t)= the record in the race and t = the number of years since 1920.
Find the linear function that fits the data.R(t)=__ (round to nearest hundreth.
What is the predicted record for 2003?__
What is the predicted record for 2006?__
In what year will the predicted record be 42.79 seconds?__
treat your data as consisting of the two ordered pairs
(0, 45.7) and (10, 45.4)
find the slope, and find the equation in the form
f(x) = mx + b form, but you will have
R(t) = .....
the procedure is the same.
Once you have the equation , for the record in 2003, let t = 83
BTW, the question is unrealistic, eventually the record will reach zero, and you will have "time-travel"
To find the linear function that fits the data, we need to determine the slope and intercept of the line.
We are given two data points: (1920, 45.7) and (1930, 45.4).
To find the slope, we use the formula: slope = (change in y) / (change in x).
Here, the change in y is 45.4 - 45.7 = -0.3, and the change in x is 1930 - 1920 = 10.
So, the slope is -0.3 / 10 = -0.03.
To find the intercept, we can use the formula: y = mx + b, where m is the slope and b is the intercept.
We can use one of the data points to solve for b. Let's use the point (1920, 45.7).
45.7 = -0.03 * 1920 + b
45.7 = -57.6 + b
b = 103.3
Therefore, the linear function that fits the data is R(t) = -0.03t + 103.3.
To find the predicted record for 2003, we need to calculate t, the number of years since 1920.
2003 - 1920 = 83 years.
Substituting t = 83 into the linear function, we get:
R(83) = -0.03 * 83 + 103.3 = 100.71 (rounded to nearest hundredth).
Therefore, the predicted record for 2003 is 100.71 seconds.
To find the predicted record for 2006, we again need to calculate t, the number of years since 1920.
2006 - 1920 = 86 years.
Substituting t = 86 into the linear function, we get:
R(86) = -0.03 * 86 + 103.3 = 100.38 (rounded to nearest hundredth).
Therefore, the predicted record for 2006 is 100.38 seconds.
To find the year when the predicted record will be 42.79 seconds, we need to solve the linear function for t.
42.79 = -0.03t + 103.3
-0.03t = 42.79 - 103.3
-0.03t = -60.51
t = -60.51 / -0.03
t = 2017 (rounded to the nearest whole number).
Therefore, the predicted record of 42.79 seconds will be achieved in the year 2017.