Question

Or these questions, non-integer answers should be entered as a decimal rounded to the hundredths place. Samantha won a trip to Europe in a contest she had entered. Rather than take the trip, she opted to take the cash value of the prize and put it in a savings account she uses as a college fund. She plans to keep this money in the college fund and let it earn interest for 8 years. At the end of 8 years, she'll use the total balance to help pay for tuition at law school. The equation below represents the total dollars, f(x), in her college fund after x years.

Answer 1

domain-
`0\leq x \leq 8\\\\`

range-
`5450\leq f(x)\leq 6588.65`

Step-by-step explanation:

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Answer 2

Domain :
`0 \le x \le 8`

Range :
`5450 \le f(x) \le 6588.65`

Explanation:

Given

`f(x) = 5450(1.024)^x`

Required

Domain:
`[\ ] \le x\ [\ ]`

Range:
`[\ ] \le f(x)\ [\ ]`

See attachment for complete question

Calculating the domain:

At the instance when she keeps the money in the college fund;

`x = 0` ---- 0 years

She plans to wait till the 8th year.

`x = 8`

Hence, the domain is:

`0 \le x \le 8`

Calculating the range:

We have:

`f(x) = 5450(1.024)^x`

When:
`x = 0`

`f(0) = 5450 * 1.024^0`

`f(0) = 5450 * 1`

`f(0) = 5450`

When
`x = 8`

`f(8)=5450 * 1.024^8`

`f(8)=6588.65`

Hence, the range is:
`5450 \le f(x) \le 6588.65`