I am supposed to model a graph without calculator from data points.

I have these data points (ages:2-20 with corresponding body mass index values):

Age(yrs) BMI

2 16.40

3 15.70

4 15.30

5 15.20

6 15.21

7 15.40

8 15.80

9 16.30

10 16.80

11 17.50

12 18.18

13 18.70

14 19.36

15 19.88

16 20.40

17 20.85

18 21.22

19 21.60

20 21.65

These points I have plotted in a graph and the from a pattern from which I should be able to make a sine function in the form: f(x)=asin(b(x+c))+d.

I am not completely sure of to find a,b,c and d. I know how to let the calculator find it, but not how to calculate it on my own. Please help?

I have calculated that d is the y length from the x-axis to the mid-point of the graph. Taking the min and max from my data points I get: (15.2+21.65)/2= 18.425

I am not sure if this i correct.. a should be the length from the mid-point of the graph to either the min or max point: 21.65-18.425= 3.225

b=(2π/period) in my example b=π/15

I know that c is moving the graph either left or right, but I do not know how to find it.

Hope I've been clear enough, first day here.. if i have been unclear please ask. I really need to get this done soon