Faisal is conditioning all winter to prepare for his college’s hockey team tryouts. He is incorporating barbell deadlifts into his daily workout regime. He plans to start with two reps and everyday he will complete two more reps than the day before. Part A: Write an explicit formula that can be used to find the number of reps lifted on any given day.Part B: If he starts with three reps on the first day, how many reps will he doon the 7thdayof training?
A. On day n, he will recruit 2+(n-1)*2 = 2n reps
B. 3+2(7-1) = 15
and that's "regimen" not "regime"
Part A: To find the number of reps lifted on any given day, we can use the explicit formula:
Reps = 2 + (day - 1) * 2
Where "day" is the number of days of training.
Part B: If Faisal starts with three reps on the first day, we can substitute "day" with 7 in the formula:
Reps = 2 + (7 - 1) * 2
Reps = 2 + 6 * 2
Reps = 2 + 12
Reps = 14
So, Faisal will do 14 reps on the 7th day of training.
Part A: To find the number of reps lifted on any given day, we need to determine the pattern in which the number of reps increases. We are told that Faisal plans to start with two reps and everyday he will complete two more reps than the day before.
Let's analyze the pattern:
On the first day, Faisal starts with two reps.
On the second day, he adds two more reps, totaling four reps.
On the third day, he adds another two reps, totaling six reps.
And so on.
We can observe that the number of reps lifted is increasing by two each day. Therefore, we can use the formula:
Number of reps on the nth day = 2 + (n - 1) * 2
= 2 + 2n - 2
= 2n
So, the explicit formula to find the number of reps lifted on any given day is 2n.
Part B: If Faisal starts with three reps on the first day, we can use the formula we derived above to find the number of reps he will do on the 7th day.
Number of reps on the 7th day = 2 * 7
= 14
Therefore, Faisal will do 14 reps on the 7th day of training.