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:

Domain : [tex]0 \le x \le 8[/tex]

Range : [tex]5450 \le f(x) \le 6588.65[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5450(1.024)^x[/tex]

Required

Domain: [tex][\ ] \le x\ [\ ][/tex]

Range: [tex][\ ] \le f(x)\ [\ ][/tex]

See attachment for complete question

Calculating the domain:

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

[tex]x = 0[/tex] ---- 0 years

She plans to wait till the 8th year.

[tex]x = 8[/tex]

Hence, the domain is:

[tex]0 \le x \le 8[/tex]

Calculating the range:

We have:

[tex]f(x) = 5450(1.024)^x[/tex]

When: [tex]x = 0[/tex]

[tex]f(0) = 5450 * 1.024^0[/tex]

[tex]f(0) = 5450 * 1[/tex]

[tex]f(0) = 5450[/tex]

When [tex]x = 8[/tex]

[tex]f(8)=5450 * 1.024^8[/tex]

[tex]f(8)=6588.65[/tex]

Hence, the range is: [tex]5450 \le f(x) \le 6588.65[/tex]

Answer:

domain-   [tex]0\leq x \leq 8\\\\[/tex]

range-  [tex]5450\leq f(x)\leq 6588.65[/tex]

Step-by-step explanation:

Got it right on edmentum

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