Question

George wants to increase the amount of push-ups that he can do each day by 2. He is already able to do 14 push-ups. The amount of push-ups George wants to do each day is given by the linear function f(x) = 2x + 12. Which explicit rule is equivalent to this linear function?

Answer 1

Explicit rule used is: f(n) = f(1) + (n - 1)d

Explanation:

We are told he currently does 14 push ups per day.

Now, he wants to increase the push ups by 2 per day.

Now, the first term in the sequence of push ups is 14 while the constant difference is 2.

Now, the explicit rule to be used here is arithmetic progression whereby;

f(n) = f(1) + (n - 1)d

Where;

f(1) is first number in the sequence

d is constant difference

n is number of days

Thus, plugging in our values from the question, we have;

f(n) = 14 + (n - 1)2

f(n) = 14 + 2n - 2

f(n) = 2n + 12

This tallies with the linear function given in the question.

Thus; the explicit rule used here is;

f(n) = f(1) + (n - 1)d