Bort is trying to get stronger. He does the following number of push-ups each day:
Day 1: 12 pushups
Day 2: 19 pushups
Day 3: 26 pushups
Day 4: 33 pushups
a) How many pushups could he expect to do on Day 5? Explain.
b) Write a recursive definition for the push-ups he does each day (include the value of the first term and the recursive formula).
c) Write an explicit formula for the push-ups he does each day.
d) Use the explicit formula to predict how many push-ups he would do on day 20 if he could keep the sequence going.
Reminder: You will be graded for showing the correct process as well as the correct answer using algebraic work.
a) To find the pattern of Bort's push-ups, we can see that he is adding 7 pushups each day. So on Day 5, he would do 33 + 7 = 40 pushups.
b) Recursive definition: Let P(n) represent the number of push-ups Bort does on Day n.
P(1) = 12
P(n) = P(n-1) + 7
c) Explicit formula: P(n) = 12 + 7(n-1)
d) To find the number of push-ups Bort would do on Day 20, we substitute n = 20 into the explicit formula:
P(20) = 12 + 7(20-1)
P(20) = 12 + 7(19)
P(20) = 12 + 133
P(20) = 145
Therefore, Bort would do 145 push-ups on Day 20 if he could keep the sequence going.