Answer:
The required function is [tex]y=11.047t+199.12[/tex].
Step-by-step explanation:
The given table shows the balance of a money market account over time.
Time (t) Balance(y)
0 200
1 210
2 220.5
3 231.53
4 243.1
5 255.26
The function that represents the balance y(in dollars) after t years is linear regression line, because the value of y increased linearly.
The linear regression function is defined as
[tex]y=bx+a[/tex]
Where,
[tex]a=\frac{\sum y(\sum x^2)-\sum x(\sum xy)}{n(\sum x^2)-(\sum x)^2}[/tex]
[tex]b=\frac{n(\sum xy)-\sum x(\sum y)}{n(\sum x^2)-(\sum x)^2}[/tex]
Put the values from the below table in the above formulas.
The value of b is 11.047 and the value of a is 199.12. Here, the variable is t.
Therefore the required function is [tex]y=11.047t+199.12[/tex].
