In 1920 the record for a certain race was 45.1 sec. In 1960, it was 44.3 sec Let R(t)-the records in the race(t)=the numbeer of years since 1920. Thank you for your help.
To determine the rate of change for the record time in the race, we can use the concept of average rate of change. The average rate of change can be calculated by finding the slope of the line that connects two points on the graph.
Let's consider the points (0, 45.1) and (40, 44.3) on the graph, where t represents the number of years since 1920.
The change in record time (ΔR) over the change in time (Δt) can be represented as:
ΔR/Δt = (R(40) - R(0)) / (40 - 0)
Since R(t) represents the number of years since 1920, R(40) would indicate the record time in 1960, which is 44.3 seconds. Similarly, R(0) represents the record time in 1920, which is 45.1 seconds.
Substituting these values into the equation, we get:
ΔR/Δt = (44.3 - 45.1) / (40 - 0)
Simplifying it further:
ΔR/Δt = -0.8 / 40
ΔR/Δt = -0.02
Therefore, the average rate of change in the record time for the race between 1920 and 1960 is -0.02 seconds per year. This means that on average, the record time decreased by 0.02 seconds every year during this period.