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]