Question

Tilly begins a running program to train for a marathon. She starts by running 1 mile the first week and tripling the number of miles each week. The number of miles Tilly will run can be modeled by the sequence An=1(3)n−1, where n is the number of weeks since she began her program. Is the sequence An a function? Why or why not?

Answer 1

Answer:

The sequence is a function as for any value of n we can not get more than one different $A_n$ value.

Step-by-step explanation:

Tilly starts by running 1 mile in the first week and tripling the number of miles each week.

Now, the number of miles Tilly will run can be modeled by the sequence $A_n = 1 \times 3^{(n - 1)}$, where n is the number of weeks since she began her program.

Therefore, in the second week she runs 3 miles, in the third week she runs 9 miles and so on.

Therefore, the sequence is a function as for any value of n we can not get more than one different $A_n$ value. (Answer)