Question

Answer the following parts asked.

Answer 1

`f(n) = 15 + (n + 1)`

Explanation:

Tina earns $15 every week when she mows the lawn.

We would put $15 because she earns $15 every week.

She earns 15 every week, so we would put (n + 1).

Our final answer would be
`f(n) = 15 + (n + 1)`

Answer 2

The explicit rule is:

`f(n)=60+15(n-1)`

After 15 week, Tina will have $270 in her savings account.

Explanation:

Let’s write down our sequence so we can see it better.

For the first week (i.e. the first term), Tina has $60.

For the second week (i.e. the second term), Tina has $75.

And for the 3rd, 4th, 5th, and 6th week, Tina has $90, $105, $120, and $135, respectively.

Therefore, we can write the following sequence:

60, 75, 90, 105, 120, 135...

Note that our initial term a is 60.

And our common diffference will be 15.

Let’s find the explicit rule. The standard format for an explicit rule is:

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

Where a is the initial term and d is the common difference.

Let’s substitute 60 for a and 15 for d. Hence, our explicit formula is:

`f(n)=60+15(n-1)`

So, to find the amount Tina will have in her savings account in 15 weeks, we will substitute 15 for n and evaluate. So:

`f(15)=60+15(15-1)`

Evaluate:

`\begin{aligned} f(15)&=60+15(14) \\ f(15)&=60+210 \\ f(15)&=270 \end{aligned}`

Hence, after 15 weeks, Tina would have $270 in her savings account.