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

Yes, because for each input value, n, there is only one possible output value.

Explanation:

Answer 2

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

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 * 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)