Answer :
Final answer:
The average score over the given time period can be found by evaluating the function f(t) = 82 - 7log(t+1) for each value of t within the range of 0 to 24 and then taking the average of these scores.
Explanation:
To find the average score over the given time period, we need to evaluate the function f(t) = 82 - 7log(t+1) for each value of t within the given range of 0 to 24.
The function f(t) represents the average score at time t, where t is measured in some unit of time. The logarithm function log(t+1) represents the time decay factor, as the score decreases logarithmically with time.
By substituting different values of t into the function, we can calculate the average score at each time point:
- For t = 0, f(0) = 82 - 7log(0+1) = 82 - 7log(1) = 82 - 7(0) = 82.
- For t = 1, f(1) = 82 - 7log(1+1) = 82 - 7log(2) ≈ 82 - 7(0.301) ≈ 82 - 2.107 ≈ 79.893.
- Continue this process for each value of t up to t = 24.
Once we have calculated the average score at each time point, we can find the overall average score over the given time period by taking the average of these scores.
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