Question

Years since 1985	1	3	6	8	9
Books sold (thousands)	4.3	6.1	10.7	12.1	13.5

I need to know the inflection and to be able to explain how I got the answer please

Answer 1

For inflection point first of all we have to calculate the equation relation of time and books.

since t=1 ,b(no. of book sold)=4.3

t=3 ,b=4.3

t=6 ,b=10.7

t=8 ,b=12.1

t=9 , b=13.5

so t=ax³+bx²+cx+d eqn 1

by putting the value of t and b we get four equations,that are

1=a(4.3)³+b(4.3)²+4.3c+d

1=79.507 a + 18.49b +4.3c+d eqn.2

3=a(6.1)³+b(6.1)²+6.1c+d

3=226.81a+37.1b+6.1c +d eqn3

8=1771.56a+146.9b+10.7c+d eqn 4

9=2205225a+182.5b+12.1c +d eqn 4

Now there are four equations and four variable ,so we can find the variable a,b,c,d

then we get the rquired equation and by puttind second derivative of t with zero ,we get the value of t

and for finding inflection point we put the value of t in second derivative exn.3 and equate it to zero,and also calculate the second drivative value by putting value slight smaller and slight greater than 1.If concavity exist then surely above t is the inflection point